Eventually, your file ends up with a smooth(ish) surface and it stops filing. Usually your file is fine; the metal isn't worn down, what's happened is residue from all the stuff you've filed off fills the rough surface. That's all the junk you now need to clean out, but it'll be in there pretty good considering the force you use a file with.
Water? Maybe - but you want to avoid rust. (and a file will chew through a Rust Eraser) Sponges? A file will tear them up. Another file! Well, kind of. Obviously another normal file will just grind and destroy both your files.
There are tools for cleaning files. They're not very expensive, and can be found at hardware or surplus stores. I found mine at Princess Auto, a rather large tool chain up here in Canada.
Looks like a filled pin cushion with a handle. The pins are weak enough to avoid damaging your files and small enough to rub away all the gunk.
Pay attention to the angle you use. You may have to rotate them to find out what works best. Files have different patterns that make up the rough areas. Sometimes rubbing with the "grain" is best, other times against.