They actually make drainage things designed to go beneath flower pots in varying sizes out of plastic, clay, etc. which you should find at a hardware store or garden shop. Most of the purpose made things have feet that hold the pot up out of the drainage water. But, like everyone's said, you can really use whatever will hold water that you have on hand.
Something I did so I wouldn't have to empty out the water from a dish I was using was put a layer of pea gravel in the bottom of the dish. The pot sits on the gravel, and the water seeps down to the bottom, and just evaporates eventually. Works great.