1) Turn amp off. Quickly twist the knob all the way back and forth about 30 times. This might be enough to wipe the crud off and buy you more time.
2) If the above doesn't work you need some electrical contact cleaner. Unlpug the amp and take apart what ever is necessary to get at the volume pot. (Remember that even unplugged there are caps in there that can zap you real good so be careful what you touch) Spray a bit on contact cleaner inside the pot and work it back and forth as in example 1. You might as well hit all the pots while you are in there. Watch out you don't allow the stuff to spray in your eyes as it comes out under pretty high pressure...wear goggles/glasses...turn your head away etc. Let the amp stand for a while to make sure all the stuff evaporates before firing it back up.
If you don't feel comfortable doing the above take it to somebody who knows what they are doing.