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It's most common to use acrylic paint on soles, which works as long as you add a sealant afterwards. There are also paints designed specifically for rubber or leather. PlastiDip is the most popular paint choice for rubber and comes in many different colors. Angelus paints are popular when painting on leather. Let the first coat of paint you applied dry. How long you wait will depend on the type of paint you used, but waiting at least an hour is a good rule of thumb. This will give the shoes time to completely dry. Place the soles on a piece of newspaper, soles up, so that they can dry more efficiently. Leaving the shoes indoors in a cooler environment will allow them to dry faster.
Choose a paint that's appropriate for the material of your soles. Wait at least an hour before doing another coat of paint. Allow the shoes to dry overnight.