How do graduate school admissions work in the US?

The short answer is, it depends. In many cases, the professor you want to work with has to have the funds available to support you. These funds are usually through grants they have successfully applied for, but in some cases, money might come from the department or university. Regardless of where the money comes from, it must be available. This dynamic means that you could be an outstanding candidate, even the best in the country, but if the professor doesn’t have money available, you won’t be able to work with them.

The best way to learn if the professor has money is to ask them if they are accepting new students. This is often done through email. See my blog post on emailing a prospective professor for tips on how to write a successful email.