If the spare went flat due to a tire bead or other slow leak try the following. If it went due to puncture or sidewall failure you're SOL.

Jack your car so the tire is off the ground. This may be easier to try with the flat spare tire off the car entirely.

Get some spray ether (aka carb cleaner), shoot some up under the rim of the tire (between the rim and the tire bead). Put a spark to it. It'll pop the bead back on and infate the tire in one shot.

Start with a little and work your way up until you get a big enough pop to do the job.

Check the pressure afterwards with a gage.

-Zeke

-STANDARD DISCLAIMER: I'VE DONE THIS MYSELF, BUT IF YOU'RE NOT 100% COMFORTABLE WITH SMALL EXPLOSIONS - DON'T DO IT!-