Wipe your ball gently with a damp cloth to remove surface dirt and grime. Make sure the cloth is not too damp as too much moisture can warp or damage the leather, causing your ball to become lopsided.
Apply a simple leather cleaner if the damp cloth does not work. Apply a very small amount and try only to rub it on areas on the ball that absolutely need cleaning. The texture of a leather ball is very important to grip and performance and applying such cleaner to areas that don't need it may have an adverse effect.
Try a cleaning eraser such as Magic Eraser if leather cleaner does not take all the dirt off of your ball. Dampen the eraser and rub it once again only on the areas that you feel really need to be cleaned.
Dry the ball off thoroughly with a dry soft cloth after cleaning, especially if you aren't planning on using it right away, as dampness will ruin the leather over time.