If the fretboard is maple (light colored wood), it may have a lacquer-like finish on it. If so, a wet (very damp) rag will do.
For anything else, you'll be able to feel the grain of the wood. For that, you can also try a wet rag and maybe add an old toothbrush for scrubbing. If it's REALLY bad (like thick, nasty gunk), you can get some Gorgomyte pads and scrub it clean with them, but that's not often needed outside of like a restoration. Once you've cleaned it up thoroughly and let it dry, some lemon oil or F1 fretboard oil - one dot between each fret, and rub in with a microfiber cloth. Let it sit for a few minutes, then use a dry part of the cloth to wipe away the excess.
Then string it up and rock!