Generally you apply for a passport at a post office. You'll need your original natz cert (make copy first), your drivers license, two photos and a check or money order for the appropriate fee. For regular service, expect 6-8 week turnaround, and for expedited service, its about 2 weeks.
For the absolute fastest service, you'll need to go in person to one of the 12 regional passport agencies (13 if you count Hawaii). The only catch is that you must have confirmed imminent travel reservations (i.e. 2-3 weeks out) and you need to make an appointment in advance.