I got a Harmony Concert off eBay, and the finish was cracked all over, the back was marred up, and the neck had funky dark stains bleeding into the finger board.
A friend convinced me to refinsh it, since the uke is all mahogany, and was otherwise intact.
I used Formby's Furniture Refinisher to remove the old varnish. I began using just a cloth, but switched to steel wool on the larger areas. The uke was beautiful under the old finish, most all of the stains on the neck came off and the back looks like new.
The next step was rubbing in Formby's Tung Oil Satin Finish with a soft cloth. I let the initial coat dry for about 18 hours, then let the 2nd coat dry for several days, then applied a 3rd coat.
The uke looks wonderful.