I learned the material first from Robinson's own book, simply titled <i>Non-Standard Analysis</i>, which I quite liked.  A few years later, I read Goldblatt's <a href="http://www.gbv.de/dms/goettingen/244289204.pdf">Lectures on the Hyperreals</a> (link to table of contents of the book), which I would heartily recommend.  Having read that, I would very much recommend <i>Non-Archimedean fields and asymptotic expansions</i> by Robinson and Lightstone, which seems to be seriously under-appreciated [only a few model theorists seem to have recently dug it up]; not the best introduction to non-standard analysis, but to me the best introduction to its connections with the rest of analysis.