Within the app, as of now, it seems a little clunky removing games from collections. You first either need to go to your library, or a collection that has the target game... open the link the for game's page, hit add to collection, then manage collections, scroll through your collections, then hit remove.
I don't know how feasible this is, but I'd find it immensely more convenient having the manage collections options/tools available in the normal collections page when you mouse-over your titles. Or, at least, the option for it to act this way.