With a sink drain, someone will have to hold a seal over the adjacent sink drain, assuming there are 2 drains. Also, if there is a dishwasher, any lines that go to the sink or disposal will need to be pinched off (vise-grips?) so that the plunger can create pressure and vacuum.
I used to have a problem with my bathroom sink clogging fairly often. Turns out the drain pipe wasn't angled down away from the sink, but was slightly angled upward, so water and crud would settle against the P-trap. Before I fixed this, I had excellent results with a little compressed air blown down the overflow drain, after closing the plunger seal. This won't work for a kitchen sink though, at least not easily. You also have to be careful and plan for the worst, as drain lines aren't meant to carry pressure.