I had two and both are gone. Clymer is the best choice (my opinion) if you cannot find the Honda Factory Manual. A set of sync gauges are a must. Good Goldwing carb parts: http://www.randakks.com/Hi Goodoni,
First, get a good manual for your bike. I bought a Clymer manual from Trike Lady and it's excellent. Val, do you have another?
As some here know, I do like to run a stiff dose of Seafoam in every 5-10 tanks just to keep jets and passageways in the carbs clean. I do not save money on air filters. I use spendy OEM Honda air filters and will not run it all the way to its service limit. Machine has to breate right.
Inspect the rubber boots for any cracking, etc. Another thing to check/replace are the large O-rings in the bottom of the metal elbows($15). Especially in older bikes like ours, they've been compressed for so long they don't seal as well as new, and you don't want any air leaks in the intakes.
Basic carb tuning for me includes setting the pilot screw to the factory spec (in the manual) and then synchronize the carbs with a four-hose&dial unit. Somebody on here might have one for sale or may be close enough for you to visit. Synchronizing means all four cylinders are pulling the same volume of air/fuel mix at each level of the throttle.