Dissolve ballpoint and gel pen ink out of fabric with rubbing alcohol before it sets.
Lay the stained area face-down on a clean white cloth or paper towels. As you treat the ink, it will transfer down into the backing cloth instead of bleeding through to the other side of the garment. Move to a clean spot of the backing as it absorbs ink.
Soak a cotton ball or cloth in isopropyl (rubbing) alcohol and blot the ink from the outside of the stain inward to keep it from spreading. Alcohol is the solvent that breaks down most ballpoint and gel ink. Hand sanitizer works in a pinch since it is alcohol-based. Test on a hidden seam first.
Continue dabbing and swapping in clean sections of backing cloth as the ink transfers down. Do not rub, which spreads it. Reapply alcohol as needed until no more ink lifts onto the cloth.
Rinse the area with cold water, apply a little laundry detergent or stain remover, then wash as usual. Check the stain before drying — heat sets any remaining ink — and repeat the alcohol treatment if needed before the garment ever sees the dryer.