Each state is different, but I believe you will have to wait so many days graduation for your school to send off their paperwork required for you to take the exam. I think it took my college about a month for my ATT to arrive after graduation.
What you can do in the meantime however is pay Pearson vue their $200, I would suggest looking on the website. It is the easiest way to pay and get your results for that matter. Then, your school should give you a packet for your state you need to register in and it will most probably have a bubble-in form that requires your full name, social, etc. Be careful with this info and make sure it is correct. Too many of my classmates had to reapply because of incorrect info not being accepted. The state paperwork is also done by money order or certified check. Look into a bank or your local post office for these. Oh and your state document needs to be authorizied. Your school can do this with a stamp.
Also, you will need your current licence and social security. If you married, divorced, changed your name for any reason, it will need to be updated correctly for the test.
If you have any other questions, I would say check with your school and if they can't answer them, ask your state.
Good luck and CONGRATULATIONS on graduation!