I use hot hide glue exclusively in chairmaking. Using PVA glues, or just about anything else, is simply madness if you plan to have well fitted joints. PVA glues will bind up in a split second in a really tight joint and will stop it from going together completely. On the other hand, hide glue will actually lubricate a joint making tight fitting ones come together more easily
You'll notice the first tool of the trade here is a good stiff bristle brush for wiping away the excess glue. This is just a cheap natural hair brush from a hardware store with the bristles cut way back near the base. Removing the majority of the glue this way keeps you from smearing it around and then worrying about getting it all wiped off. Also, try to avoid adding any water to the surface as you clean so that you do not dilute the glue and spread it around even more. That said, slightly damp cleaning tools may help lift the glue better.
Your next tool is going to be paper towel for cleaning the joints. This may prick your eco-friendly conscience but a clean surface each time to remove the glue is, in my opinion, the only way to go. Using a wet rag will only spread it around for you to fuss with later before finishing. Plus, a paper towel will pick up the glue off the surface better than a rag.
Lastly, be sure to use something like an old magazine under your work so that you don't damage the side that is on your workbench.
I first learned most of these methods from Peter Galbert. If you have heard about his upcoming book from Lost Arts Press and are wondering what to expect, this is the sort of detail that he covers. It seems nothing is left to guesswork.
Even though I read and helped edit most of the text early on I can't wait to get my hands on the finished copy. Chris and Megan did a really great job of compiling the book into a super easy to read style that is a hallmark of LAP publications. Plus, Pete went back and reworked a lot of the drawings and I haven't seen all of those yet. Very eager. Come on Chris, get that thing to the printers!!!!!