There is a short introduction by Mikhalkin: http://arxiv.org/abs/0709.1049 expanded in more detail in this book: http://www.math.toronto.edu/mikha/book.pdf (the link is now outdated; this may be the same book: https://www.math.uni-tuebingen.de/user/jora/downloads/main.pdf )
The Oberwolfach lecture notes by Itenberg, Mikhalkin and Shustin are also nice.
