A waterproof sealant such as GE Clear Gutter Caulk is easy to use ... or long stick to dislodge leaves and other debris from inside the downspout. You might need to run a strong blast of water ...

Then count up the inside and outside corners and end caps ... overlap and splice together gutter sections. Lay a bead of gutter sealant along the corner 1-1/2-in. back from the edge.