Use a tee to remove dirt
You can use an old golf tee or your can use a larger toothpick to remove spots of dirt from the dimples of the golf ball. Dig in those dimples and knock the dirt off the surface.
Try the ball washers that you find at most golf courses. These ball washers give you a combination of water and bristle brushes to clean the balls. They usually can clean off most golf balls with little trouble. You will need a towel to dry them because there is no towel attached to the ball washer in most cases.
Soap and water solution
If you have a great number of balls to clean -- and you may if you have gone on a scavenger project in golf course water hazards -- your will need a bucket of soap and warm water. Let the balls sit in the soap and water solution for at least five minutes before rinsing them in warm water and drying them.