i'm not a fan of chemical uncloggers ... some things i've used are
plunging to pull the clog up higher so i can get it out with plumber's snake and/or bent coat hanger
even a bottle brush sometimes works ... the little fibers catch on the hair and you can pull it out ... all gross
dump 1 cup of baking soda into the drain, pour in 3 cups of boiling water
or
1 cup baking soda, 1 cup vinegar ... after the fizzing ... pour in 3 cups of boiling water
or baking soda, followed by boiling water, followed by vinegar
make sure the vinegar is white vinegar and not cider vinegar only because the white vinegar seems to have less of an odor that lingers
after the drain is clear, put in a hair catching drain insert ... i had little mesh/screen type things that you push down into the drains. just get in the habit of cleaning them out after each use (only takes a minute) and saves you aggravation and clogged drains. the mesh thing will fill up quickly but is easy to clean out. i had them in sinks, bath and kitchen, as well
good luck!
edit:
here ... they call them strainers or mesh sink drain traps.