I did some research, here's a real answer for anyone interested:

Hair clippers are designed to be self-sharpening. As the metal blades glide past each other they rub together, continually honing a sharp edge as you cut. Nonetheless, under some conditions, clippers can get dull. If the blade is not oiled and cleaned regularly or if it corrodes, it can become dull.

Just take the blades off and brush away and dirt or hair, then scrub it with rubbing alcohol if there's any rust on them. Put the blades back on and run the blades for five minutes or so.

Basically, you do it the exact same way that you would an electric trimmer.