This process is what I had to do on my 2002 Kawasaki Vulcan Drifter 800. It should be the same for all 800 models from what I can tell. Also, some Harley Davidson bikes use this same carb, or a very similar one from the same manufacturer, so this should help the Harley crowd out as well.
I used a DynoJet jet kit part# 2186. I have a K&N filter and Hard - Krome pipes on the bike. For the most part, any jet kit you get will be done exactly like this.
Your first order of business is to remove the carb from the bike. Sorry I do not have a write up for that but it wasn't that hard.
With the carb off the bike take it to a work bench or table. There will be some springs and smaller parts so don't do it over grass or gravel or something silly where you'd lose a part if it fell to the ground. Or maybe stopping in the middle of your product to crawl around on the ground for an hour looking for a part the size of a needle is your thing?
Now, let the fun begin!
The first step in removing the needle is to remove the black plastic cover, outlined in yellow in the image. It's held in by 4 phillips head screws. Be sure to use the correct size screwdriver on these. Mine were a little tight and I could see these being a possible disaster is you stripped them.
Remove the spring, shown above, and the vacuum piston, shown below. Inside the vacuum piston there will also be a needle and a plastic needle holder.
This is what you should be left with.
In this picture I've outlined in yellow, the needle, and needle holder. The vacuum piston is the item in the upper right corner of my work mat.
Next you'll take the new needle, spacers, and e-clip, included with the jet kit, and follow the instructions. The new needle will have several grooves cut into the top of it. For my application, it called for an e-clip in the #3 groove with 2 washers resting on top of it.
You can now reassemble the vacuum piston, needle, needle holder and cover. The installation is simply the opposite of removal.
Now for the installation of the new jet.
First, turn the carb upside down and locate the 4 phillips head screws, circled in yellow below, holding the float bowl on. Remove the screws using the proper screw driver making sure not to strip them.
Once the screws are removed simply remove the float bowl. Below is what the carb will look like with the float bowl removed. I've circled the jet in yellow.
The old jet is easily removed using an open wrench and the new jet is simply screwed right back into the same threads the old one came out of. Some kits come with different size jets so be sure to read the instruction to determine what jet to use. The jet size should be stamped right on the jet.
Put the float bowl back on and secure it with the 4 screws and move onto the next item.
Pilot (Fuel Mixture) Screw Adjustment
The final step to the jet kit install is to adjust your pilot screw. If you skip this step you'll have a very poor running bike.
First, turn the carb upside down and locate the metal mixture screw cap ,circled in yellow in the next two pictures. Once the cap is located drill a hole in it (the jet kit comes with the drill bit). NOTE: STOP DRILLING THE SECOND IT GETS THROUGH THE CAP OR YOU'LL DAMAGE THE MIXTURE SCREW UNDER IT!
The yellow box in the picture below shows the screw in the hole.
Once the cap is off adjust the screw per your instructions.
Ta-da! Your new jet kit is in and all that is left to do is toss the carb back on and enjoy a smooth running bike!