Here is a short introduction, and an even better one
Papers by May
An introductory article of Greenlees
An interesting article on different approaches to the “smash product problem”: http://www.math.uiuc.edu/K-theory/0319; see also http://www.math.uiuc.edu/K-theory/0320 for the corresponding model structures.
http://mathoverflow.net/questions/4561/what-is-the-intuition-behind-brave-new-algebra
nLab page on Brave new algebra