SeaFoam is your friend... Get a can of it, and add according to directions, to both the fuel tank, and the crank case.
For the fuel system, it will help dissolve varnish deposits within the entire fuel system, but it won't dissolve everything, unfortuntely; it is the easiest thing to try, though. Run that tank of fuel down as low as you can, before filling up, to get the most out of it. It can really help if the varnish is not too much, or clogging the jets. It's easy, and inexpensive (~$9 per 16 oz. can).
For the oil, add the correct amount to the crank case, start the engine, and run it for five minutes, on the center stand; with the rear wheel spinning freely, let the engine idle, and shift through all five gears, to thoroughly flush the transmission, as well as the entire engine, of deposits. It will dissolve varnish, carbon, and other crud, within the engine, and the transmission. The crud will be dissolved and float in the oil, being captured by the filter, as well as being suspended within the oil. After five minutes idling, the oil will reach 170-180 F, which is when it suspends deposits within itself. Then shut it down, and change the oil, and the filter -- if it wasn't black when you started, it will be at this point, with all of the crud it loosened from the engine, and the transmission.
If you have to let the bike sit for more than a couple of weeks, without being ridden, treat the gas with
SeaFoam, to stabilize it, and to prevent formation of deposits within the fuel system (up to 12 months only -- after that, the gas will turn to crud...). Periodic treatments in the gas tank, will help ensure a clean fuel system, so I recommend adding it at least once per month, during riding season, as a preventative measure. Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII