Commercial brand drain cleaners are very toxic and dangerous to have around if you have little children. Try these ecofriendly clog clearers from Earth Easy instead.
Light duty cleaning: Mix together 1/2 cup salt and 1 gallon water. Heat the mixture (but not to boiling point) and pour it down your clogged drain.
For tougher clogs: Dump 1/2 cup baking soda down the drain. Follow it with 1/2 cup vinegar. The chemical reaction will cause the fatty acids and soap to break down. After 15 minutes, pour 4 cups of boiling hot water down the drain. (Caution: Do not use boiling water for plastic drain pipes. Use hot tap water instead. Also, do not add a commercial drain opener while the vinegar is in your pipes. The results can be noxious fumes.)
If you still haven't cleared the clog, I've found using a Zip It super helpful for pulling up clogged hair. But, be forewarned, you may gag a little.