I've tried this method several times, it always works.
Step 1: Gather Tools
All you need is an old toothbrush and some hydrogen peroxide.
Step 2: Pour It In
Make sure the drain is closed and pour enough hydrogen peroxide to cover the drain.
Step 3: Let It Soak
You will see it start to foam up, let it sit there for about 3 minutes.
Step 4: Scrub
After about 3 minutes, take your toothbrush and scrub around the drain.
Step 5: Drain
Drain it and run the water.
Step 6: Ta-da!