Typically, the best way to clear a drain line in the most safe and effective manner would be power rodding. The plumber would remove the drain assembly under the sink including the J-bend, P-trap, and tail flange piece. That drain-pipe would be cleared of any debris. Then the plumber would use a cable power rodding machine or pistol rod handheld machine and run the cable into the drain opening. The machine will then spin through the line and break up any debris in its way or catch hair and other debris so that it could be pulled back. The rest of the debris will be pushed through the line to the larger drain and out towards the main. This will restore full flow to you drain and the sink will drain and flow out with full force. Once this is complete and the line is open, the plumber will reassemble the drain piping and clean up the area.