I've never used one, but I know that many people do. What you will need is a tank (~$30), a regulator (~$20), a moisture trap (~$20), and an adapter to go from the outlet on the tank to your airbrush (the "Tire Chuck Adapter" pictured on this page MIGHT work, but I'm not certain: http://www.dixieart.com/Hoses.html#anchor287927)
Edit ... Correction: Actually you'll need an adapter to go from the tank to a 1/4" NPT thread for the regulator and moisture trap. You may then need an adapter to go from 1/4" NPT threads to your airbrush. Also throw in a roll of Teflon tape to make the connections air tight.
If you don't mind some noise, you can get a decent compressor from Lowes, Home Depot, or WalMart for under $100. They will normally already have a regulator but you'll still need to add a moisture trap. Look at the ones with a tank, not the little ones for inflating car tires and such. They won't last long.