Clean the damaged area of the rubber roof using window cleaner and rags. The chemicals in window cleaner should remove most or all of the dirt and grime from the EPDM material.
Squeeze some liquid dish soap into a bucket and fill with warm water. Scrub over the damaged area on the rubber roof using a scrub brush to take up any residual window cleaner and to get a clean surface for the patch to bond.
Open a can of rubber roof cement or polyurethane sealant and scoop out enough to cover and overlap the hole in the rubber roof by about three inches using a trowel or putty knife.
Spread the rubber roof cement or polyurethane sealant with the trowel or putty knife. Apply more rubber roof cement or polyurethane sealant as necessary to completely fill the hole in the rubber roof as well as overlap it by a few inches.
Allow the rubber roof cement or polyurethane sealant to dry according to the manufacturer's suggested drying time. Your rubber roof is now sealed and should no longer leak.