Climb up to the roof wearing a safety harness and helmet to help prevent injuries if you slip.
Sweep the roof with a broom to remove any loose debris that can interfere with the repair process.
Apply rubber neoprene cement to any cracks in the roof's flashing or chimney. Neoprene cement usually comes in a tube similar to caulk and is applied the same way, with the trigger on the caulk gun pushing the sealant out of the tube and into the cracks.
Repair larger damage with a roof patch. It applies like a tar, and you then smooth it over the area with a trowel. Push a fiberglass cloth into the repair so it's flat against the damage and held in place by the roofing material. Cover the cloth with a second layer of patching and smooth it with the trowel again. Allow the patch to fully dry.
Mop the roof with a roofing tar solution. This helps seal smaller cracks and breaks that you may not have noticed. Start in the far corner of the roof and work towards the side where your ladder is so you don't have to walk through the wet tar to get off the roof. This is usually a temporary solution but it buys you time for a full roof replacement.