Squirt the heck out of the shifters with WD40. Do both while you're at it. I think it helps to take out the shift cables to do this. Squirt in the holes vacated by the cables. Work the shifters in between dousings. If the shifters don't shift without the cables in them put a cable in them without the housing and pull on the cable while you shift them. Take the cable out, douse again, etc. Sometimes this won't get the shifter working right away but they will work the next day after the lube has had a chance to do it's thing.
Also, do the same to the front derailleur. Squirt the heck out of all the pivot points. Work it by hand in between dousings. I've had front derailleurs so gunked up that it seemed like itwas a problem with the shifter but in reality was a problem with the derailleur.