Clearing a slow or completely clogged shower drain is usually pretty easy. There are only 3 common types of pipe used for shower drains. They are-
The 2 inch plastic shower drain will either be ABS or PVC. While these plastic drains don't readily catch hair, the drain body at the shower base may. If that occurs it's a simple matter to lift the hair strainer and scoop the blockage out of the drain opening.
Here's a tip to help you avoid losing the tiny screws down the open shower drain. Your shower drain top plate may be the kind that's held down with tiny brass or stainless screws that aren't magnetic. Put your foot over the grate portion of the drain while removing the screws. Once they're out, set the screws aside where they won't fall down the open drain while you're working. When resetting them, use your foot again to cover the opening.
A shower drain is more likely to become plugged if it's been plumbed with iron pipe. Iron pipe will catch hair, and a cable drain snake is the best solution.
The shower often has a 1 ½ inch iron P-trap, the same kind that often makes it harder to snake a clogged bathtub drain. But the direct access provided by the shortness of the tail piece, and the knowledge that nothing is falling apart down there makes it easier to just push the cable though the tough spots.
The hair will usually be massed at the sanitary tee. Luckily the toilet is usually located nearby. The 3 or 4 inch pipe that serves the toilet is as far as you need your cable to reach. It shouldn't take too many feet of cable to clear your clogged shower drain.