Plug the overflow drain (wet your hand and press against it) then run
some water and use a plunger. I bet you get a whole buch of evil
smelling crud coming up the drain into the sink...
Hair, soap scum etc. Skundge buildup.
If the sink has one of the built-in lever driven plugs, disassemble and
remove it. Betcha it's filthy.
Use a drain cleaner, plunge, drain cleaner, plunge. If you still have
the problem, disassemble and clean/replace the trap and/or the sink.
Life. Nature\'s way of keeping meat fresh. -- Dr. Who