Finding a used fixed gear. Lots of ways to do this. First you will have to decide do you want a true track frame or do you want a converted road frame. Either will do, here's the difference. The track frame will have a little higher bottom bracket so you can use a slightly longer crank then the road frame however I don't recommend anything longer than 170mm crank length. Remember your going to be pedaling through the corners the longer the crank the more chance you have of scrapping it and possibly crashing. Also you want to be spinning and not struggling pushing a big gear. A track frame will usually have a quicker harsher ride than the road bike. Track frames will be harder to find than road frames and probably more expensive. If you decide to convert a road frame it must be the older style frame with horizontal drop outs. The dropouts are where the rear wheel axle rests. The older frames had dropouts that allowed for an inch or two of adjustment. Meaning you could slide the wheel to and fro in the dropout. Newer style frames have a verticle dropout which drops right down on the axle with no forward or backward play. This you don't want! When setting up a fixed gear you must have some room for adjustment. The reason: when you cut your chain you have a set length of chain.You have to be able to pull the chain tight on the dropout. With a horizontal dropout you can do this on a vertical you can't!
Chain tension is very important on a fixed gear you have to have this space for adjustment. Just look at a track frame. A road frame will have the dropout opening facing the opposite direction from a track frame but this is fine you can still pull the wheel tight.
Do not use a quick release on your rear wheel! Your rear wheel must be securely bolted fixed gear chain puts a lot more pressure on the rear wheel. Several ways you can do this 1) use a regular track wheel with the bolts. 2) Change out the quick release axle for a bolt on axle 3) or they make a bolt on that slides through the quick release axle. If you use this system use a chain tensioner as well as a safety measure. In fact I recommend a chain tensioner on all fixed gears. A chain tensioner is a bolt tensioner that goes on either side of the dropout. It has a nut you tighten. As you tighten the nut it pulls the wheel tight. So if your bolt was to go loose on the wheel the chain tensioner would still keep your wheel in place.
Now where to find your frame or bike- garage sales, Ebay or Craigslist.
Try to find a frame that hasen't been wrecked. If you get a bent frame then it may be a headache to straighten. So look for signs of a crash scrapped paint, dents etc... Also ask the owner he may tell you the truth, but then again he may not! It never hurts to ask!