You just have book an appointment and get to a consulate. We were going overseas with some friends and a few nights before, one of the people realized their passport was so close to expiring they were likely to be denied entry (many times countries will not let you in if your passport could expire while you're there). They booked an emergency appt. in ATL, drove the 6ish hours, then got their flights changed to leave from ATL. They got it same day if I remember correctly, and flew out that night or the next morning.