How is a wormhole formed by spacetime surgery? How is a wormhole formed by performing surgery on spacetime?
 A: You will probably turn up more information online using the term "topology change" rather than "surgery." The original work on this was by Geroch and Tipler. As far as I know the state of the art is described by Borde 1994, which generalizes and unifies the previous results. The basic result is that  unless we have CTCs or an energy condition is violated, we can't have topology change. That means, for example, that a universe that starts open must stay open, and you can't create wormholes that don't already exist.

How is a wormhole formed by spacetime surgery?

I'm not clear on what is intended by the word "how" here. You can certainly draw "pants diagrams," for example, showing a universe forking off into two universes, so the "how" is simply that kinematically, there is no problem with describing this kind of process. The nontrivial results have to do with why it can't happen.
Borde, Topology Change in Classical General Relativity, http://arxiv.org/abs/gr-qc/9406053
A: You should read Michio Kaku's "Hyperspace", there is a lot of info on wormholes in "Hyperspace". In his book, he does state that theoretically we could open a wormhole, but only with large amounts of heat. We are currently not able to harness the massive amount of energy and heat in order to open a wormhole, but maybe in the future we will find a way.
