The humble drain snake (or "zip-it" tool) is a long, flexible plastic strip with barbs along the sides. You push it down the drain, twist it around, and pull it up.
Imagine a small, spring-loaded claw on the end of a long stick. You push it down, squeeze the handle to open the claws, release to grab the hair, and pull it out.
But 9 times out of 10? The culprit is a big, nasty wad of your own hair. Grab a snake, hold your nose, and reclaim your dry shower floor.