Actually, there are carb syncing tools that use metal slides instead of mercury. But to take that a step further, its actually not all that difficult to make your own carb syncing tool, just give it a quick google and there will be a host of sites explaining how to do it with some vinyl hose, connectors, and oil. Perhaps this summer I will attempt to make one and write a howto.
I'd start by setting the air/fuel mixture screws. Does the thing run like crap? you mentioned having to do something with the floats. maybe you need to replace the needles and seats if it appears as though they are letting gas run in. However, if that were the case the bike would either be pouring gas out the overflow or not run at all.
Hershey is one of an elite few that really know what they are talking about when it comes to carbs and things of that nature. Not to be rude or anything, but I'm kind of hesitant to agree with stang68's instructions.
If you really aren't that mechanical at all, carbs are NOT the place to practice. If you can't afford to pay to have someone fix it, try and find a friend that has a better idea of how everything is supposed to work, grab a service manual and thoroughly familiarize yourself with what you are working with before doing anything.

 

Carburetor Synchronization can be found on page 3-9 (pg 25 in most downloaded copies) of the Honda CBR600 F 91-94 Service Manual.

You can also check out these links:
http://www.cartestsoftware.com/fz1/c...onization.html
http://www.angelfire.com/ia/z/FZ1carbsync.htm


I think I took pics when I did mine...but never uploaded them.