Forget everything you know about clearing clogged sink and tub drains. Throw away your snakes, plungers, and drain cleaners. There are only two things you need to know about clearing clogs, and neither one of them will cost you a dime...
First, it's a good idea to be proactive. If you notice that the water is draining a bit slower, fill the sink, tub, or other offending vessel with cold water. Then open the drain. Usually, the weight of all that water is enough to clear a minor clog. If not, fill the sink or tub again, open the drain, and use the cupped palm of your hand like a plunger to add a bit of pressure. This will clear most clogs.
No luck? Bring out the big guns. Connect your garden hose to an outdoor spigot. Drag it to your sink or tub, even if they're located on the second floor. Poke the hose in the drain, and stuff a towel around it. Have a helper turn on the outdoor spigot. After a few seconds, you'll hear the sweet swishing sound of freely draining water. Guaranteed.
Okay, so you may not want to toss your plunger. It may still come in handy for toilet clogs, but the hose trick works there, too. And it works for clogged dishwasher drains as well. I once talked an appliance repairman into trying it. We had to open the access panels, undo the drain hose clamp, and use duct tape to attach the hose to the tubing...but it worked like a charm.