It depends on your state, but you almost always are required to take a fairly challenging written test (very rarely a road-skills test for permit). Usually you are required to be accompanied by a parent or legal guardian who must sign some forms for you. You often must bring a birth certificate, proof of residence (like a utilities bill, phone bill, that has your address on it, etc.), and sometimes another form of identification (passport, identification card, student id, etc.). You will most likely have to pass a vision test, so if you wear glasses, even for reading, be sure to bring them with you. Some states will require you to acquire a signed form from your school stating that you are in good academic and behavioral standing.
If your mother kept her maiden name, sometime this is a problem for legal matters (stupidly enough, it was for me), so you might have to drag your father along instead.
Often there is a small fee every time you take the written test and to cover the cost of the card.
It is highly advisable to read a motor vehicle guide (available at your DMV) before taking the permit test.
Find your state's DMV website for more information.