There are a few ASL signs for garbage, but the best sign looks like the form of a trash bag hanging in a frame. Take your non-dominant forearm and lay it out flat to act as a frame, palm facing down, then take your dominant pointer finger while the rest of the hand is in a fist, and form a 'U' shape with it under the "frame", as if forming the outline of a trash bag.
Like puppies, babies often find an unsettling level of fascination with the garbage bin. As they grow older, they will enjoy putting things in the garbage bin instead of rooting around in it. You can use the sign for garbage to tell them to put something in the trash.
This is a really nice sign to teach our toddlers when we are asking them to complete simple tasks as they learn to be helpful.