First thing is to get a good manual for that bike. I like the Clymer M504 manual. Very thorough.
Pull the carb set off, clean the outside thoroughly, so all linkages are clean and smooth and you won't get crud on the inside when you open them up. Pull off the top caps, exposing the throttle valves with the diaphrams Joe mentions, remove them and check for hole/cracks and suppleness. Also check the ends of the needles for goo and damage. Then pull off the bowls from the bottom of the carbs. Keep all parts for each carb together. Inspect the main jet and low speed jet for goo and damage. To function properly everything in there has to be clean. So, I pull the jets and clean them with GumOut, clean and inspect the seats, blow out all fuel channels, and reassemble.