Check out Fixedgeargallery.com
They just finished a contest to build a fixie for $147.83 or less!
They have photos of the 10 or so bikes that were built, most have great descriptions about how they were made up for 147.83 or less.
Remember, this is bicycle mechanics, the easiest way to learn is to take it apart, keep the pieces in order, clean each piece up, grease it, and put it back in the same order.

I have built a single speed from a mountain bike, it wasn't difficult.
I plan to build a fixed gear later this year, probally on the same sort of budget as you.

Good Luck!