First of all, you should know that the weber is almost identical in anatomy to the dell'orto carb used as an example in the haynes manual for the 2-stroke piaggio scooters and which is posted on the wiki links
2-Stroke Carburetor Set-up Technique So you shouldn't get too hung up on finding instructions for this specific carb - opening it up and cleaning it will work the exact same way, with the parts looking more or less the same.
I've attached a version of your photo with numbers on it. The order you address the numbers isn't crazy important - they are more there just to refer to specific steps. These steps are for removing the carb - after that point you can open up the float bowl on the bottom, unscrew the jets, and clean them.
so:
1) this silver screw tightens a clamp holding the carb into the black rubber intake boot on the top of the crankcase. Loosen this screw quite a bit so that the clamp flops around.
2) this brass screw holds the throttle into the carb. Undo this screw to pull the throttle cap, cable, slide, and needle jet out of the carb as one unit. These can be further disassembled if desired, but shouldn't be necessary for your purposes - just wrap a paper towel around them or something to keep it clean and gently rest the assembly on the engine out of the way
3) this rubber boot is the intake to the carb from the airbox. It can be pulled off of either the carb body or the airbox. It doesn't matter which for your purposes (pulling the carb off the bike)
4) disconnect the 3 hoses from the carb. The number 4 is next to the gasoline hose. The other black hose is the vacuum hose which opens the fuel tap as the engine turns over. The little clear yellow-ish hose is the oil pump feed line - this is how 2T gets into your carb. The vacuum and oil pump hoses connect near the number 2 on the picture. All 3 hoses can be pulled off easily - on my scooter there is a hose clamp with a screw for the fuel hose, which must be loosened to get it off. The other two have a pinch clamp. Assuming yours is the same, but just go with the flow if your clamps are something different. Don't drop or lose the clamps, and feel free to reuse them as long as they still... clamp. I personally leave the pinch clamps on the vacuum and oil hoses, because they don't seem to want to fall off, but I pull the fuel hose clamp off since it will fall off if left to dangle.
Make sure gunk from your engine area doesn't get in the end of these hoses, especially the autolube, because the scooter will run "normally" with this hose obstructed until it scores the cylinder or seizes up. As will all mechanical work - keep things clean
5) this is your autochoke. You can either unplug it from the wiring loom (the plug is hidden inside a black protective rubber sleeve along the wiring toward where the it enters the body of the scooter on the right of your picture. On my scoot it was about 2/3 of the way toward the entrance to the body. You can either A) cut this sleeve off to access the plug, making sure not to cut the wires beneath, B) try to fold it back out of the way to access the plug, or C) remove the autochoke from the carb body where the #5 is placed in your picture.
To do the latter, there are two brass screws near the base of the autochoke holding it onto the carb body. You can see one halfway between the screws for #1 and #2. Undo these screws and a half-moon piece of metal which was clamping the autochoke onto the carb body will come off. Then *gently* pull the autochoke out of the carb body - it will want to stick in because it has an o-ring to give it a good seal in there. Gently and slowly pull it out, being careful not to mess up the plunger of the autochoke which sticks down into the carb. If you leave the autochoke hooked up to the wiring of the scooter, definitely gently wrap it in a clean paper towel before resting it anywhere and make sure it doesn't get knocked. You don't want to mess up the delicate plunger.
At this point, the carb can be jiggled out of the rubber intake boot which you loosened the clamp on in point number 1. Just lift and jiggle it toward the left of the picture and it will pop out of the boot. Careful, if you flip the carb over at this point any gas in the carb will dribble out the top where the throttle went in. You can either let this happen, or keep the carb upright and loosen the drain screw at the very bottom of the carb float bowl. Either way, gas is going to come out, so pick a good place for the gas to go (it's not a ton... maybe a couple of tablespoons?
Anyway, this will get the carb off your scoot and ready to open up. To put it back on, reverse the process.