Sure thing King Cronin!
It's pretty easy really. You can only make reservations 4mo in advance, so for a trip like this, you really need to be on it, as lots of people are planning spring and fall trips. The summers can be oppressive, and the winters can be brutal.
So get on the NPS reservation system, pick the dates and campsites, then fill out the details much like an online ordering system. NPS will send you a confirmation email with a link to pay the $30 permit (do it within 48hrs or you lose your reservation). It's a little weird the first time you do it, but isn't it that way with all good things? ;)
Once you take care of that, you simply head down there and check in at the Visitor Center and pick up your permit, as well as pay your 7-day park entrance fee, which is $30 for 4WD, $25 for a motorbike, and $15 per foot/pedal bike..