There is a slight difference between the repairing process of aluminum gutter end caps and standard assembled gutter runners. The aluminum ones have a cap at the end of the gutter that stops water from exiting the gutter.
First remove the end caps off the gutter usually using a rubber mallet to detach them.
Use a flat screwdriver and remove all the sealant that remains on the edges of the gutter.
As soon as you finish cleaning the gutter edges you can apply silicone on the grooved channel around the edges of the gutter. When you finish applying the silicone you can take the new cap and push it hard on the gutter and around the edges until it is completely sealed and glued with silicone. At the end remove the extra silicone and clean the gutter.