In this video, This Old House general contractor Tom Silva has a fast fix for a dripping rain gutter.
1. If the existing aluminum drip edge is pressed tight against the fascia board, shim it out with ⅜-inch-thick x ¾-inch-wide x 8-foot-long strips of pressure-treated wood. If necessary, use a table saw to rip the ⅜-inch-thick strips from a pressure-treated 1x6.
2. Slide the wood strips behind the drip edge.
3. Fill the joint between the top edge of the gutter and the fascia board with silicone caulk.
4. Smooth the bead of caulk with your finger.