A slow-draining shower is more than just a nuisance; it can also be dangerous. Water that collects on the base of the shower waiting to drain is usually full of soap, which settles and collects on the surface. Even if you clean this off periodically, slow-moving water also promotes the growth of mould and other slippery slime. A clog or poor venting may cause the sluggish draining.
Hair is the most common cause of clogs in shower drains. It collects in the curved pipe under the drain called the P-trap and often catches on the strainer. It is difficult to remove with a plunger and usually collects other debris like soap and dirt, eventually stopping the drain completely if you don't do something about it. Clogs can develop even in the absence of hair, however. Sometimes a partially-used bar of soap or a cap from a tube of toothpaste finds its way past the strainer and lodges in the P-trap, collecting other debris and slowing water flow.
Poor venting in the waste lines can also cause water to drain slowly from the shower. Venting is required on all waste lines to allow air in to replace the vacuum caused by water flowing down the drain. When the vents are blocked or inadequate, the vacuum can be strong enough to hold the water back. A symptom of this condition is air bubbling up or down the drain as the water seal is broken just long enough to allow it to escape. Slow flow from poor venting allows sediment to settle in the P-trap and promotes clogs.
While a plunger won't have much effect against hair, it will remove most other clogs. It is most effective if you use it while there is at least an inch of water in the bottom of the shower. You can also remove most clogs, including hair, with a plumbing auger, or snake. Remove the strainer, and feed in the snake until it won't go any farther, then crank the handle to work the head through the obstruction. If the drain is full of hair, most of it will come back with the auger when you pull it out of the drain.
If you suspect that the venting is obstructed, you can often clear the vent lines by going on the roof and spraying water from a garden hose into the vent openings. You may also find that the vent openings themselves are obstructed by leaves or other debris. Chemical drain cleaners will dissolve obstructions in the drain line that are out of the auger's reach, but some are highly caustic and may damage the pipes and the environment. Instead of a caustic cleaner, use an enzyme-based one or a solution of baking soda and water. They work more slowly but are safer to use.