Here's the advice I give to all the undergrads who contact me asking about how to get into graduate school. People have different follow up questions, so I'll monitor the comments section of this post if you have specific questions. 

Credentials: I'm currently completing a PhD in Psychology and Neuroscience at Princeton University. I also got PhD offers from Columbia and Boston University. I was shortlisted at Harvard and Stanford, but I told them I was going to take my Princeton offer so the advisors I applied to didn't "waste" their admission slot on me. (I include this just as an example of how complicated graduate admissions can be.)  

How to get in

1. Get as much research experience as possible before you apply. Summer internships are the perfect time to work in a lab. If your university offers class credit for working in a lab during the semester, do that as well. You are applying to be a full time researcher, so research experience and publications are the most impressive things to put on your resume.
2. Being a research assistant/lab manager in a lab will look great on your resume; it will also be a VIP ticket to that lab when it comes to application season. It is very rare that RAs who want to stay to be graduate students are not able to stay in their labs. This is a thing you can do for a year or two after graduating university.
3. You can also apply for post-baccalaureate research fellowships for the year or two after you graduate university. The NIH runs a good post-bacc program you can look into.
4. Good grades are important, but research experience and publications can make professors look past mediocre grades and/or standardized test scores. 
5. PhD applications include a personal statement or statement of purpose (SOP) that describes what you want to study. This is a critical part of your application. If you aren't sure what you want to study or how to choose a high impact research topic, consider applying for coaching from Effective Thesis!
6. What does a good personal statement/SOP look like? Identify at least one professor at the school you're applying to and explain what interests you about their work. For example, "I am excited to apply to Brown University because of the groundbreaking work Professor Shenhav has done on cognitive control. I would like to apply his expected value of control theory to better understand decision making in different clinical populations."
7. "If you have multiple research ideas, considering writing more than one (i.e. tailored) SOP and submit the SOP which is most relevant to faculty at each university."(ht jacobpfau) The more your personal statement targets a specific faculty member at the school you're applying to, the more that faculty member will want to admit you to work with them. 
8. For your personal statement, avoid vague thoughts about your future like, "It has always been my dream to study the human condition at a beautiful Ivy League university." Professors don't care about this. Professors want to hire somebody who will immediately start producing publishable research. Instead, structure your personal statement to explain your research skills, e.g., "I developed my data analysis skills by analyzing economic trends in R for my senior thesis," and your specific research interests, like: "I want to explore the psychological impact of growing up in poverty by studying the development of schizophrenia in different income brackets."
9. For STEM programs, try to learn as much stats and programming as possible, both before and during graduate school. In your personal statement and CV, highlight all the stats and programming skills you have. They're super useful and professors don't want to spend time teaching you how to code, they want people who already know how to do this. For biological sciences, linear algebra, Bayesian statistics, and mixed effects regression models are all super helpful to learn. Python is the most useful and versatile language to learn across all disciplines. R is popular for statistics, but you can do most stats in Python too. Matlab is popular in academic environments but is declining in use. A lot of legacy code is written in Matlab, so chances are you will encounter it if you inherit legacy code from a senior student.
10. Understand the structure of the program you're applying to. Are you applying to work with a single professor, as you do in Princeton's Psychology program? Or are you applying to a committee and will you be spending your first year rotating through labs, as you do in Princeton's Neuroscience program? If the former, you need to write your personal statement as a letter basically directly to that one professor, as they will be the only one fighting to admit you to the program. If the latter, you will need to write a little bit more generally about your interests. Be sure to mention at least 2, but ideally 3 professors. Don't mention more than that if you can't explain why you would want to work with the extra professors. But if you can, great, add them!
11. Study for the GRE, if it's required by your program. I got a GRE practice book, worked through the whole thing over one summer, then took the test. GRE scores are less important than publications, but some programs have minimum scores and will block your application (even if a professor wants to admit you!) if you don't score high enough. Other programs are dropping GRE score requirements. Be sure to check your program requirements.
12. Consider applying for funding before applying for graduate school. Students with funding are very attractive at admissions, and there are some schools that don't pay you a living wage unless you have an external fellowship. There are EA funds available for graduate students working on high impact projects (which you should be doing!). Governments have a lot of fellowships to fund graduate students. If you are a United States citizen, look into NSF funding.
13. As soon as you know you want to apply to a specific list of programs, let your recommendation letter writers know. Say something like, "Hi Professor X, I just wanted to let you know that I'm applying to these five schools for a Physics PhD. The earliest deadline for these schools is November 1st. Would you comfortable writing me a recommendation letter?  If so, I will put your name in the application system. Thank you so much for your time, I really appreciate it!" Give your recommenders as much time as you can to write their letters, and maybe give them a reminder 3 weeks before the deadline. It's pretty rude to demand a letter a couple of days before your applications are due, and you don't want them to be angry with you while they're writing!
14. If you impress schools with your application, you'll be invited for interview days where you will chat with professors at each school. One of these meetings will be with the advisor you want to work with. (Or more if you indicated you wanted to work with multiple specific professors.) For visiting day interviews, "bringing up concrete ideas on next steps for a professor's paper is probably very helpful" (ht jacobpfau). It shows you understand and are interested in the research they are considering hiring you to do.
15. Don't worry too much about your interviews with professors you didn't apply to work with. Obviously impressing them is a good idea, but you don't have to become an expert in domains that you didn't discuss in your application. These interviews are mostly just to check that your personality isn't impossible to work with. For these interviews, you can steer the conversation more towards the culture of the department instead of talking about specific papers. For example, you can ask about how much collaboration happens between labs and what kinds of resources the department has access to.
16. Last bit of visiting day advice: don't get drunk at visiting day. These events often serve copious amounts of alcohol, and nervous applicants sometimes drink too much and act unprofessionally. 

Choosing a program

1. Your advisor is the most important choice you can make. Talk to as many people as possible in the lab before you join it. If you and your advisor do not get along, your experience will be terrible.
2. As ryancbriggs points out, program prestige is also important. Going to a more prestigious program will make it easier for you to get better collaborators, better funding, and better jobs after graduate school. If you have massive amounts of uncertainty about which program to attend, just picking the most prestigious program you get accepted to is an excellent heuristic.
3. It's dangerous to go to a place with only one advisor you want to work with. You never know what might happen. Your PI might not get tenure, they might get sick (mine almost died!), they might get a job offer somewhere else, they might lose funding, you might not get along, you might lose interest in your original project, etc. You need a backup plan. Unlike undergraduate programs, you can't really transfer between PhD programs, so you're stuck at whatever university you start at. You can usually still switch advisors within a department though, and sometimes jump between departments within a university.
4. Pay attention to how students in different places treat each other. There are some places where people compete in ways that are really unpleasant. The other graduate students will be your friends and often roommates, so go to a place that's supportive.
5. Ask concrete questions about funding and teaching. Programs do not like to be upfront about this. Find out how much time you will be able to spend on research vs. teaching to get paid. Find out how students feel about their course load and training program.
6. If you have a specific population you're interested in (e.g., clinical patients, veterans, children) make sure you go to a place with access to these populations.
7. If you have a specific technique you want to learn, make sure you go to a place with *good* access to these resources. There's a big difference between having a dedicated research scanner in the basement of your office building vs. having to take a bus across town to use a hospital scanner. Don't let PIs (who don't have to do this hands on research) make these kinds of struggles seem easy, your life will be hard enough without complicated logistics!

Should you even go to graduate school?

1. Can you do what you want to do without a graduate degree? If you can, maybe just do the thing! If you want to do cool AI Alignment research and already have the skills to be hired by Redwood, DeepMind, Ought, etc., why don't you just apply straight to the job that will actually have a positive impact? Chris Olah doesn't have a Ph.D. and he certainly doesn't need one after working at Open AI, Google Brain, and Anthropic (which he co-founded!). If you change your mind later, you can usually apply to graduate school after you get some real world experience. Most programming jobs or anything that gives you solid data analysis skills look great on resumes, and might actually increase your chance at getting into a top program later.
2. If you are good enough to get into a PhD program, you are good enough to also work in industry or in non-profits. Consider applying for non-academic jobs AND academic jobs. If you get a non-academic job offer that really appeals to you, seriously consider that career path. Don't think that you are only qualified to do academic work and are thus trapped into going to graduate school.
3. If you do not have a specific research interest, you might not be ready to apply for a PhD. Processes for coming up with a high impact research topic are outside the scope of this post, but check out Effective Thesis for inspiration. You don't want to waste your time studying something "useless" so it is extremely worthwhile to get feedback from the EA community on your research agenda.
4. Ph.D. students are more anxious and depressed than the general population. Partially this is because academia attracts anxious/depressed/perfectionist people, partially this is because academia is terribly structured: it's hard to get accurate feedback on your work, it's easy to get stuck in a project that produces no results but eats up all your time, and you have almost no recourse if you are treated badly by your colleagues. Everybody thinks they'll be the exception to the rule and will actually be super happy in their program (otherwise why would they even apply?), but you should keep in mind that the average student is not happy.
5. Financial security is massively underrated by the average EAs I speak to. People who go to graduate school are generally more motivated by truth seeking than money. But remember, you will make approximately $30,000 a year for 3-7 years while your similarly talented friends who go into industry will make over $100,000 per year. You might think that all you need is a laptop, internet connection, and place to sleep, but in 3-7 years you might want to do something else, like start a family or a company. Look into daycare and living costs in your area. Would your stipend cover these costs? Will you be able to save enough money to have some runway after graduation? Is financially supporting your family important to you? Graduate school might make you very unhappy if so.
6. Remember you are not getting paid in money. You are getting paid in intellectual freedom to work on projects you're excited about. In that vein, only apply to schools you actually want to attend. Don't waste your time interviewing at places you aren't excited about. Being paid $30k a year to do something you don't love is not worth it.
7. If you're not excited about the places you got into, consider applying again next year instead of doing a program you are not excited about.

Don't get stuck

If you get into a program and then realize that you're wasting your time, you can always drop out of graduate school. If you're deeply unhappy in graduate school but don't want to drop out "because you're the kind of person who completes academic courses" (ht Robert Miles), take a moment to consider what you value about your personal identity. Some super wonderful Effective Altruists dropped out of their Ph.D. programs and proceeded to have majorly positive impacts on the world (e.g. Katja Grace), so you can definitely be an über EA without a PhD. Remember, your goal should be to have a positive impact on the world, not to get some fancy letters after your name ;)

Good luck!