I live in a house with three women with long hair. It's not uncommon for me to have to take apart the drain on the shower every other month to untangle a ball of hair that has been keeping the water from flowing.
The Drain Weasel is a cheap tool that allows you to instantly fix hair-clogged drains with a patented 360-degree swiveling head. It works much like a drain auger, except smaller and more convenient.
The [Drain Weasel comes in 3-piece set for around $6, and is highly rated on Amazon.