Rough-running / misfire-esque are 90% incorrect air/fuel mixture, the bane of carburetors. In most cases, slime in a jet or nozzle is the problem, and they can be a bear to correctly clean. Easy fix is just to replace the carb, most are under $40, but depends on the engine.
Get me the serial number off the side of the the engine "GXXX-1234567" and I'll get you the part number and price for a new carb, gaskets, etc.
When installing the new (or cleaned) carb, always use new gaskets. It's easy to get a tiny vacuum leak.
If you *really* want to clean the old one (or if a new one is too costly) get a can of real carb cleaner and some compressed air; here's a link on another forum on How To Clean A Honda Carburetor:
How To Clean a Honda Carburetor - Lawn Mower Forums : Lawnmower Reviews, Repair, Pricing and Discussion Forum