Replace the stuff inside. You should be able to get a kit. It's pretty basic to rebuild. You may need some snap ring pliers. Getting the brake bled after replacing is the hardest part. I use my thumb to create a little back-pressure on the bleeder screw.
Man, I get the stuff all over me when my bike gets stuck, upside down, on a ledge above me and I'm trying to pull it down.
Where have you looked so far, KX rider? Your dealer should have a kit. If you looked in a catalog like Tucker Rocky or something, most of those cut off at 88 or 89. They will list parts for fitting 88 up, but some parts fit other years prior than the ones listed. I don't know enough about KX 80's to tell you what will, though.