Plungers and Augers
One of the most useful tools for plumbing emergencies is the plunger. Flat plungers can be used to loosen clogs in sink drains, and open-flange plungers work well on toilets. When you use a plunger, wear safety goggles to protect your eyes from any debris that might splash up – particularly if you've been using drain cleaner. Make sure there's enough water to cover the top of the plunger, and work the plunger up and down to force water through the pipes.
Another handy plumber's tool is the snake. The snake is coiled inside the housing and can be extended for several feet. To use the snake, push the extension piece into the drain until it reaches the obstruction, and lock it in place with the setscrew. Then hold the pistol grip steady, and turn the handle to rotate the extension. You may need to rotate the extension piece to force it past bends in the pipes. For toilets, consider a closet snake, which has a curved end to help send it through the curves in the toilet drain.
For clogs in larger pipes, you might want to use a blow bag. A blow bag can be attached to a garden hose and then pushed into a drainpipe to the point of obstruction. When the water is turned on, the blow bag expands to fill and seal the pipe, and water pressure forces out the obstruction.