Okay, this 1936 Silvertone 1970AE will be my first major cabinet restoration:



As you can see, part of the grillework on the left-hand side is missing. There is also a long, deep gouge in the top, visible as a light mark in the photo just to the left of center on the top panel (about 3" long by about 3/16" wide by 1/16" deep) that looks like it came from a circular saw blade. What would be the best way to repair these flaws? Is there some sort of illustrated guide online or in a book that tells how to proceed? The radio was free, and I am not looking to re-sell it, but I don't want to sink hundreds of dollars into it, either. I just want it to look nice again.

First thing I would do is strip the cabinet. Replacing the grill parts looks like it's going to require some thought and planning. I'm not a woodwork pro and if I were you I'd try to find someone local who works in cabinetry to advise you. Most of all enjoy the process!
Ben