Locate the points of the leak. The leaks are obvious during rain and could be noted at that time. Make repairs when conditions are dry.
Clean the area of the aluminum gutter around the leak using a detergent with a degreasing agent. Allow the area to dry.
Apply a tri-polymer-based caulk to the leaking seam of the aluminum gutter, on the inside and outside of the gutter. The caulk adheres to itself, which will allow you to apply a second bead of caulk over a previous application to close larger openings. Apply the caulk along the gaps or holes in the aluminum gutter using a caulking gun.