Radio Shack sells contact cleaner, a spray that you can use on the potentiometer. As mentioned, open the unit up so that you can immerse it from the inside of the component.
The knob that you actually turn to increase/decrease the speaker volume shuold be physically connected to the potentiometer (abbreviated and commonly refered to as a "pot") so if you can manage to pop/remove the knob itself, the pot. would be behind/underneath it. The best way would be able to open it up and spray it on the inside, you could also try to just use the straw that is on the contact cleaner and try to get under the knob itself.
With canned air - if you have it. The knob you turn is connected to a short shaft (pole), which is connected to a round metal case (about the size of 4 nickels). Some have holes where you can aim a tube from a can.
It's still dirty. Although it might not be possible, if you could put some pressure on the knob (sideways) as you turn it the static might get louder, or be gone!
Contact cleaner is better, but I just figured that you'd have canned air lying around rather than contact cleaner.