Summarize:

Most tub and shower pipes are small and easiest to unclog with a small, hand-held auger. These augers are easy to handle and flexible, which makes them great for pushing through narrow and angled pipes. These are available at all home improvement and hardware stores. There are two types of small plumbing snakes: drain augers, which are common small augers that have a round compartment with a long coil of wire in it, and closet augers, which are shorter and mostly used by plumbers to unclog toilets. A closet auger does not have the round compartment on it and so the wire length is much shorter. Choose a drain auger when getting a clog out of your tub or shower drain. In addition to an auger, you'll need supplies to open up the drain and to clean up any water or debris that is in the drain. Get a bucket, screwdriver, wrench, and rubber cleaning gloves and put them near the drain. Also, have a few old towels around to clean up dirty water. Many tub and shower drains have built in stoppers and screens that need to be removed in order to access the pipes. Unscrew any cover plates and disassemble any stoppers in your way. Every tub and shower stopper is different and thus comes apart differently. If you can't figure out how to take your stopper apart, do some internet research about your specific type of stopper. When inserting a snake, push the snake wire into the drain while simultaneously turning the handle on the back of the tool. This will turn the wire as you push, allowing it to move further down the drain through any clogs. Some snakes only turn when the wire is in a locked position and can't be advanced. If this is the case with your snake, push the wire in a few inches and then lock the tool and rotate the wire. Repeat this by unlocking the wire, pushing it in a few more inches and then relocking and turning it. As you lower the cable, move your grip down until it's about 3 inches (7.6cm) from the drain opening. This close grip allows you to control your motions and feel for the clog easier. Once the end of the snake hits the clog, turning the handle will push the hook at the end of the cable into the clog so that it can be grabbed. There is no need to turn the handle quickly. Slow and steady pressure on the clog will work most effectively. As you pull the cable out, turn the handle on the snake so that the cable rotates. This will help the cable move around bends in the pipe. Pulling the cable out of the pipe slowly will help to keep the clog hooked to the end. Run the water through the drain. It may take a few seconds to wash away the remnants of the clog, but it should begin to flow quickly. If the drain is still obstructed, snake the drain one more time. Insert the wire into the pipe once again and spend more time trying to hook the clog to remove it. If water still won't run through the drain after you've snaked it several times, it may have been pushed further down into your pipes. In this case, it's time to call the plumber.
Choose a small auger made to snake tub and shower drains. Gather the additional supplies you'll need. Remove any drain stoppers and screens in the drain. Insert the auger wire into the drain. Turn the handle on the snake to break up the clog. Pull the snake out of the drain slowly. Determine if the drain is still clogged by pouring water down it.