The Fretboard 65 Lemon Oil
is the guitarist's choice for both removing dirt and grime from the fingerboard as well as keeping it in great condition for a long while afterwards.
Once you've removed the dirt and grime from your fingerboard (the best way is to use a soft toothbrush and a toothpick (neither will damage the wood)), the Lemon Oil will keep dirt away by providing an invisible sealant against stains and moisture. Be careful not to overdo it, just a dab on a soft cloth will be fine for in between each fret, and a careful application once a year is sufficient to keep your fretboard in perfect condition.
Warning: not for use on Maple fretboards. For Rosewood or Ebony, it's great!