Carbs can be finikity little buggers.
You need to pull them apart, check the settings against Andy's spec chart, and then make sure that all the jets and orifices are spotlessly clean.
Pay attention to the needles and throttle slides (especially MC18 & 21). Look for signs of wear. These bikes are old now. many with a high mileage and I've seen quite a few that run bad because of dodgy needles and throttle slides.
Andy doesn't mention float heights, which although very important seems to get forgotten on many occasions. Start with 12mm float height, and if it's still a little foggy off the bottom then go to 12.5mm then 13mm.
I use an excellent carb cleaner from Permatex, doubled up with an ultrasonic cleaner (thanks Mike) to make sure that everythings nice and shiny.
However, my 'old' tools consist of a bunch of cotton buds, pipe cleaners and the frayed end on a throttle cable for poking down into the little holes.
Brasso on the cotton buds and pipe cleaners can bring things back into life, but don't be too savage as you only want to get rid of the poo, not the brass itself!
Leaky float needle valves can be restored if the damage is minor by fine valve grinding paste, mixed with oil on the end of a cotton bud, spun at low speed with a drill. Just cut enough to clean up the face and no more. Doesn't always work, but cleans up small corrosion. Then polish with Brasso.
Make sure that the rubber tip of the needle valve is clean and soft. I use contact cleaner and a soft rag to wipe away any deposits here. Gently now or you could knock the tip off which is a pain in the bum.
Synching the carbs is quite straight forward. and can be done with the carbs off the bike. Wind up the idle screw so that you can just sneak the unfluted end of a small (say 2mm) diameter drill bit under the slide. jiggle the adjuster screw around until both slides are equal. Then check at full opening that both slides hit the top at pretty much the same time. Concentrate on the small opening rather than the WOT setting.
All that's left is to make sure your air filter is clean and oiled and you should be good to go.
Sometime there's a problem with the small filter hidden under the airbox that the white thrree way plastic joint plugs into. It's a paper filter and if your bike washing technique is a bit too thorough then this can soak the filter and suffocate the air solenoid circuit. Easy way of checking is to unplug the joint and run the bike to see if any problems are resolved.
Bit of a long post this, but I think that's covered most of it.