I just went through this for the first time myself this past week. Look on here and find the thread "another one for you old Bear guys" (or something similar to that).
I have pictures on there of what my efforts did on three bows I received free. First off I washed them all in dish detergent to get the 40 years of dust and grime off. The Tamerlane I took a tube of the white toothpaste (not gel) and polished it with damp T-shirts. The Grizzly I used fingernail polish remover (acetone) to get the paint off it, then used toothpaste, and finally car wax to put a shine on it.
I wish I would of taken pictures of that Tamerlane before I started, you would never believe it was the same bow, and that toothpaste would do that. But I do have before/after pictures of the Grizzly, and I am still working on the Kodiak Mag (I had holes to fill on it).
I did learn to use the toothpaste just like I would personally use it. Put it on with a damp rag and the bow being visibly wet. I just polished it like I would a car and then rinsed the toothpaste off. I did not put it on the riser wood of the Grizzly, I could feel the wood grain with my thumbnail and I was afraid it would get into the wood grain cracks. I used 0000 steel wool on that part and it cleaned it up nicely.
I have sanded the K-Mag down completely with 150 sandpaper, but very lightly over the writing on it. I bought Minwax wipe-on poly gloss per what I've read on here, but I haven't made it that far with it yet. And I can't answer how long to leave one strung up beforehand, my own cautious nature is to usually leave it a day or so before I put my face up there and give it a release!
I have found that this is fun stuff, and my wallet is afraid it won't be the last time I do it.