You can make your own tarp-tent using instructions from Ray Jardine at
www.rayjardine.com.
Another way to go cheap is to use what you already have. Make that old tent, old sleeping bag, etc. last for one more trip.
For short trips, the cost of the gear is more significant. For longer trips, there's bigger bang for the bucks worrying about the costs on the road. A big saving strategy is to camp all the time, and camp for free as much as you can (i.e., avoid campgrounds that charge a fee). And eat as much as you can out of grocery stores. And skip the high-priced luxuries such as soda, beer, ice cream (i.e., all those things that make life worth living).
It's important, however, not to go too cheap. At the extreme, it becomes conterproductive. Remember the famous Click and Clack axiom that says "It's the stingy person who spends the most."