What product should I get to clean the finger board and frets for my guitar?

Lemon oil.  It cleans and also provides moisture for the fretboard.

My luthier told me that he used olive oil.  That is what i have been using on my 1987 classical guitar with great results. I also use it to wipe my guitar since it has very thin french polishing finish (matt). As Tony mentioned in his update, it also provides moisture to the wood.