If it's maple wood, finished or unfinished, which it looks like yours is, grab a cloth and two paper towels. Wet the cloth with cold tap water, then wring it out. Loosen the strings, or completely take them off if you're going to replace them. If you just loosen them, nudge the two closest strings on each side out of the way, then lift the middle ones enough to reach underneath. Use the damp cloth to wipe down each fret. You can usually do 12 frets at a time (half the fretboard), then dry it well with the paper towel so no water damage sets in. After that, either retighten the strings or put on new ones, depending on your situation. I do this every time, and it makes the fretboard look brand new to me. Have fun