There are other schools of thought out there that you should use a more interrogating product such as steel wool (finest grade possible) or plastic wool (which is less harmful) to ensure that the real hard stuff that’s caked onto the fret board gets taken off, as well as try and polish off each fret.
You should cover up the metal pickup covers to avoid the particles of steel wool from sticking to them magnets! It’s very hard to get micro steel wool off a magnet one by one.
Myself, I prefer to leave these techniques to the professionals for if the steel wool is abused, it can cause a lot of damage. If a little extra elbow grease is used it produce the same results, and is less destructive to the guitar.
A formula of 1/3 vinegar, 2/3 water can also work well for the stronger grime. I’ve never tried this, but I’ve heard on forums that it’s a great trick. So, use at your own caution.
Mineral oil is also recommended and can be found more easily than some fret board oil, applied in the same fashion.
To apply the oil or other products, drip a few drops onto the cloth (use a clean cloth for every new chemical used) then rub it in. We don’t want to saturate the fret board, rather just apply enough to ensure that the fret gets a very light oiling, its not an engine. Most manufacturers say ‘just a light layer’ is required.