The CVK carburettor is produced by Japanese manufacturer Keihin (whose name is derived from the second character of the word "Tokyo") for several motorcycle brands, including Kawasaki. Although it was primarily designed for low production cost, the CVK has a track history of good performance, easy maintenance and simple tuning.
The hardest thing about tuning the CVK carb on a Kawasaki is simply getting to it--there's only about a 3/4-inch clearance between the mixture-adjustment screw and the starter motor. There are no off-the-shelf tools to help you, but you can improvise by placing a high-quality 1/4-inch wide flathead screwdriver into a vice and bending the tip. You may need to heat the metal shaft to red-hot with a butane torch as a precaution against breaking it.
There's a simple method If you need a baseline for factory tuning. Gently screw the pilot or idle mixture screw until it just begins to bottom out. Be careful not to damage the carb by over-tightening. Once the screw is tightened, back it out of the carb by one and 7/8 turns to the factory position.
Follow the same procedure for setting the factory tune, but back the screw out by 2-1/2 turns. This will typically yield the best throttle response off-road, but may cause bogging on the pavement if you're in too low of a gear. This approach tends to work best in lower altitudes. You may find the mixture a bit rich in higher altitudes.
Idle Drop Method
Tune your carb to the "off-road" position as above, and take the bike out for a short ride to warm the engine. Back at the garage, set the idle speed to between 1,300 and 1,500 RPM, turn the idle screw in until the engine begins to stumble, then back it out until you find the highest idle speed. Then turn the mixture screw in until the idle drops about 30 RPM. This should coincide with the highest engine vacuum to yield peak engine efficiency.
Exhaust Gas Analyzers
If you want the highest tuning level, you'll need an exhaust gas analyzer. An oxygen sensor voltage of .49 volts will give you an almost perfect 14.7:1 air/fuel ratio; an increase or decrease of 0.1 volts will correspond to a 0.5:1 change in air/fuel ratio. A carbon monoxide percentage of .60 indicates a 14.25:1 air/fuel ratio; add or subtract 0.25:1 A/F ratio for every 0.7 change in carbon monoxide percentage.