OK well first I'd do a basic check of a few things like spark (unscrew one plug, reconnect it to the wire, hold against engine and crank, should have spark), battery voltage (should be >12.5 with bike off), and wiring (none chafed, broken, corroded, or on fire) before you tear into the carbs. If all seems well then cleaning the carbs is probably next.
Once you're committed to a carb cleaning (which I still consider likely to be needed), go
HERE and scroll down to "CB500/550 Shop Manual" for an electronic copy of the manual. Also grab the parts book for your bike, and the "Honda Common Service Manual".
Finally, download the
Honda Carburetion Manual which is available in the
Technical Library on the main website.
Once you've done your reading, mostly you'll need a phillips screwdriver, a flathead screwdriver, solvent, brushes, and lots of patience

Start by pulling off the carb rack, then flip it over and take off the float bowls. You should be able to judge condition right away, parts should be clean and free of debris. Unscrew and clean out the jets and float valves, then re-assemble and reinstall. See where that gets you.
mystic_1