Nothing. That's the beauty of nature and the human body. The socket fills with a clot and that eventually turns in to bone. Nothing else is needed!
Your teeth. Extractions for orthodontic treatment are used to find space to align the remaining teeth. The "holes" are closed by moving teeth into them, leaving a nice bite and smile.
Nothing. The idea of extracting teeth for braces is that there is not enough room in your mouth for all the teeth. The spaces will be eventually closed by moving other teeth into those areas and straightening them.
Usually nothing, but. Almost always nothing is done, as we are constantly closing the gaps during therapy. However with extremely self-conscious patients or aspiring models, i fabricate a false tooth fastened to the adjacent tooth. I put a brace on it it to blend in. After all, i was a dentist before i became an orthodontist, so it is easy to do. As the gap closes, i thin the fake tooth down until un-noticeable.