There are multiple stages for graduate school admission. There is being admitted to the school. And there is getting a professor to agree to be your advisor. (Or supervisor or whatever it is locally called.) There might be more layers, such as getting admitted to candidacy for a specific degree. Any or all of these may involve an interview. Or it may be somewhat less formal. You might simply wander by the prof's office, buttonhole him/her for a while, have a chat, and then the both of you agree that you should work with that prof. It will depend on the school and the department and in some cases the current faculty and how formal they are feeling. Many things about grad school are very different from school to school. My grad work, for example, did not have a language requirement, while other science PhDs in the same university did.
In any case, some homework before you even apply to a grad school is a good idea. Find out about the research interests of the profs. If you can, read a few of their papers and be as familiar with their work as you can. The website
http://arxiv.org/ may be a big help there. Google the prof, check out Google scholars and any other resource you can find in the time you have. Also get some magazines like Physics Today and similar things. Get the issue that shows recent grads and where they got positions and find the ones you would like to emulate.
Once you find a prof who might be interesting to you, contact that prof and see if he/she has room for you. If that prof already has nine students, you may not want to be number ten. Be sure to ask the prof what sort of preparation they will find interesting, what research they are currently working on, and whether you would be a good match for them. Be sure that prof knows what degree you are thinking of, what degree you are working on right now, and any other academically important items.
Once you have a few possible places to study, contact the graduate school offices at the interesting universities. Tell them which degree you are interested in, and ask for specific details on the admission procedure. Also ask about things like scholarships that may be available, and any other financial matters. For example, many scholarships don't consider you unless you apply. Find out about tuition fees, opportunity for employment as a grad student, where you might live, etc. Lots of schools let you do teaching duty for some hours each week and pay you for it. Doubly good because it counts on your resume and it helps pay the rent.
Once you find a combination that interests you, apply as soon as you can.
