1. For a general overview of modeling count variables, you can get free access to the video recording of one of my The Craft of Statistical Analysis Webinars:
2. One of my favorite books on Categorical Data Analysis is:
Long, J. Scott. (1997). Regression models for Categorical and Limited Dependent Variables. Sage Publications.
It’s moderately technical, but written with social science researchers in mind. It’s so well written, it’s worth it. It has a section specifically about Zero Inflated Poisson and Zero Inflated Negative Binomial regression models.
3. Slightly less technical, but most useful only if you use Stata is Regression Models for Categorical Dependent Variables Using Stata, by J. Scott Long and Jeremy Freese.
4. UCLA’s ATS Statistical Software Consulting Group has some nice examples of Zero-Inflated Poisson and other models in various software packages.