I would like to preface this with, if you find anything other than varnish-like deposits in the bowls, like particles of rust, etc. you should back-up in the fuel delivery system and remedy that as well, such as check the petcock screen, check the gas tank and possibly install in-line fuel filters (small plastic see through things you can get at any MC dealer and splice them into your fuel lines). Note they usually have an arrow on them indicating flow direction. That said..
1) Where are the floats? (okay, after you are done laughing could you please tell me exactly how to get to the floats? i know they are in the carbs, but still confused.)
The floats live inside the bowls. They hang down within the bowls on pivet pins. You will see them once the bowls are off.
2) Can I do this while everything is still installed on the bike or do I need to take the carbs off the bike? I see the first step is to undo the brass screw/plug at the bottom of each bowl, but can I do this while it's on the bike? Won't the gas then leak over the engine?
Some have serviced the bowls, floats and float needles on the bike, but I prefer taking them off, makes the rest of the work easier. If you elect to take them off, shut off the fuel at the tank, of course, and remove the fuel lines from the carb bank. I use a small can (like a tuna can) to catch the fuel as you unscrew the drain screw. Personally, then I pour it into the lawnmower.
3) What materials do I need to clean the bowls and check the float height?
Some carb cleaner is the best thing. There is a very good chance you will need to go further than just cleaning out the bowls, so I would recommend getting some Yamaha carb cleaner, any Yamaha dealer or multibrand dealer that includes Yamaha should have it. You can try some spray carb cleaner from an auto parts place first if you like and see if you need to dip any other bits in cleaner. If so, then get the Yamaha. I use a small steel rule with a sliding "T" on it for measuring the float height, it is scaled in MM and inches. Available at almost any decent hardware store. Sorry I can give you some insight on the float height as I'm fumbling with my own at the moment.
4) A posting in the Faqs, suggest you should have new gaskets since you'll probably need them. Is this true, and if so, can I get gaskets at a local motorcycle shop?
Depending on how old the current gaskests are, there is a good chance you will need new ones. If they are dried and cracked to stiff, go for new ones. Even with new ones, when you get ready to install the bowls again, apply some pressure to the bowl and wiggle it around a bit before you snap the locking bale bake on.
Good luck to you. I personally don't get along with carbs, I lack the required Zen I guess.