1. Purchase the student ADC membership from the Apple ADC Store.
2. You'll get an e-mail that tells you that you need to verify your student status.
3. You scan your I.D. and schedule and e-mail or fax it back to Apple.
4. Your membership becomes active (takes a few days usually, unless you call ADC relations --- then they will do it right on the spot).
5. You'll get an ADC welcome kit in the mail with a t-shirt, documentation and the current version of Mac OS X (unless they changed it to download only now).
6. You'll also get a "Hardware discount asset" placed in your ADC account that's good for one-time only. The discount varies on different products. You should also keep in mind that you can purchase software from the ADC store at a discount (Aperture is significantly cheaper) as long as you have the hardware discount asset. Once that's gone, you can no longer purchase anything else from the store (or a least that's what they told me).
I haven't been a member since 2003, so some things have likely changed.