Remove airfilter and it's case (two bolts under the air filter), the carb should be exposed. I believe honda has two ot four long bolts on top of the carb (remove carefully, there is a gasket that you may be able to preserve). Carefully remove throttle and choke controls (little metal bars attached to the carb). There will likely be one hose on top (remove it carfully, it will have some fuel in it. While disconnected, spin the motor with the starter to check if fuel moves through the pump and out of this hose. Prepare to catch fuel as it is pumped. If fuel doesn't pump, then start with the pump) one larger hose on the right side (remove it) and then a wire attached to the botton (wire should have some slack, follow it and loosen it to give more slack or unscrew the sensor where it enters the bottom of the carb). There may be a little tube on the bottom (disconnect if needed).
Carb should be able to move freely. There are 4 bolts on the face (remove carefully, there is a gasket that you may be able to preserve). This will help you access the fuel nozzles. Remove 4 screws on the bottom of carb (careful not to damage the rubber seal inside). The float tank is in the bottom.
Once disassembled, take carb cleaner to it like it's your job! Spray everything! Spray in the nozzles, spray the butterfly valves, spray the float tank, and spray into the bottom of the carb while moving the float tank up and down! Soak it in a carb cleaner solution if you've got one (be careful with any non-metal parts!). If you find something in there I didn't mention, spray that too!
Reassemble! Hope that helps. It may be worth taking to get serviced if this scares you a little! If that's not an option, make a trip my way and I'll try to walk you through it. I was in Valdosta and Thomasville this week, but I don't plan to head back to Georgia anytime soon.