If tightening the nut 1/8-1/4 turns at a time doesn't stop the leak than the nut should be removed. The drain also should be removed and the flange piece (that sits in the sink) needs to be cleaned.
Apply fresh plumber's putty to the underside of the flange. Place it back in the basin and press down until putty oozes out.
Place the rubber washer and than the nut back on to the threaded drain piece. Snug it up by hand and than tighten with a wrench until the pipe can't be turned by hand.
Clean the putty from the flange and fill the basin with water. Open the drain and look for leaks. Tighten in small increments if leaks are noted and continue running water until no leaks are found.