The following page will give you the locations of tests given in your area by the ARRL - there are other VEC organizations, but

http://www.arrl.org/arrlvec/examsearch.phtml

You go down when they are running a test, pay your test fee (I think it's up to $17 now). You sit down and take the test in from of 3 "Volunteer Examiners" - when you are done (the test is untimed), they will collect your test, and grade it right there. Either way, they will let you know if you passed or failed. If you passed, they send the results off to the FCC, and in a few days to a week or two, if you follow the list of "New and updated licenses" either on the FCC web site, or one of the ham sites that tracks it, you will see your name, and your call sign. As soon as the call sign is publishe, you may get on the air - a couple of days later, you'll get your license in the mail

The fun part? Let's assume you passed. For no additional money, you may then sit your "general" and if you pass that, your "extra"

If you are upgrading, the process is similar, but you bring your existing license with you. If you pass, you may start using your new priviliges right away, but you add a /AG or /AE at the end of your call, which tells the listener "hey, even though the database has not been updated yet, I passed" - and you will probably get a big "congrats" over the air