[From Thom Baguley]
More in Thom's book at https://seriousstats.wordpress.com/2012/02/. Chapter 17 focuses on generalized linear models (mainly Poisson and logistic regression).
As far as a quick and dirty sample size calculation goes you could take the square root of the counts and use a normal approximation* (i.e., the method that you'd use for regular ANOVA or t tests). For anything fancy it is more elegant to use simulation - but there will not be much gain from the quick and dirty approach unless you have a lot of information about the problem.
* The Poisson distribution has a single parameter that is both mean and variance - the square root transformation is well known as a (very) approximate normalizing transformation in this case.