You need a sex of Hexxies, metric to get the front piece offa the cylinder, but it's not so hard as you would think...lemme see if I can recall this offhand...
First, unscrew and remove all the plastic crapola, cause you have to in order to get a screwdriver set to pull the side panels....then pull the side panels.
Turn OFF the fuel, at this point.
Then , loosen the drive chain...I do this by loosening the back wheel and just slipping the chain off.
Next remove the forward two of the three main bolts that hold the transmission housing to the frame, they should be 13mm on both ends.
Loosen, but do not remove the last bolt, the one that has part of the kickstand hooked up to it.
Now you can gently pull the transmission casing down, and actually get to the carb itself.
Loosen the screw at the front, where it hooks up to the input to the cylinder - this allows you to turn the carb sideways to remove the two screws at the top, remove those, and you can pull out the throttle cable piece...but watch not to tear this little paper gasket under that plastic piece, also, take a good look at it as you remove it so you know how the spring goes and all when you put it back.
Now, you don't have to do this next bit but it makes it a damn lot easier....that black rubber thingie over the back of the carb....simply find the metal ring holding it on and loosen that screw...and it pulls off - this'll give you more room to get it out.
The gasline piece comes off easy, but make sure not to foul or tear that little strainer piece in there, or lose it.
The oil line onbolts from the top of the cylinder input easily from that angle as well, keep an eye on the paper gaskets and where they are as you pull em.
Then, find the right hexxie and remove the four little bolts that hold the input to the cylinder, I am not sure if that has a gasket or not, without goin back out there to look, so keep that in mind.
At this point you can just pick up the carb and walk off with it to clean it.
Now, others probably have better ideas, but I soak mine in a mix of warm water and Dawn dishwashing liquid and scrub clean with a gun-cleaning "toothbrush" cause I don't wanna upset the roomies with the reek of industrial chems.
Reverse the proceedure to get it back in, save this...
That black rubber piece on the back of the carb HAS to line up with the front of the "Airbox?" or whatever that black plastic gadget is back there....easiest way to do that is to take a flathead screwdriver and use it to guide then together as you raise the trans assembly slowly with yer left hand.
I'd do a lot better showin you than tellin you, but I hope that is some help.