I usually use Draino or Liquid Plumber, then after that is done I will take the drain cover off and use some plyers to pull out and hair chunks still lingering at the top. It is gross but it works like a charm.
My husband is a plumber and the safest, easiest, and cheapest way is to use your plunger...Take off the flip switch on the wall just above the drain that you use to plug or unplug the drain and put a plastic bag over the hole to prevent any air from getting in...Plung the exposed drain while holding the bag there for suction. I works wonders!
Wow staci, our souls must really be connected cause my shower is clogged right now too! LOL! I tried drano and it didn't work at all. I'm going to try the stuff that turns into a foam. I think its liquid plumber. I've used it before and it worked well.