In a very brief summary Zombies Anonymous is: 'Sad, funny, poignant, shocking, horrifying and revolting' and concerns the life, death and undeath of Archibald Griest.
In a little more detail: As a member of the undead, even though he retains his faculties, Archie is rejected by family, friends, work colleagues and has no legal rights. In fact, as a zombie, there’s no washing–up to do. Archie forms a support group called Zombies Anonymous to discuss this new state of supernatural existence with other zombies including: The problem of slowly rotting; the predilection of the living to bury you while you're asleep and whether Chanel No. 5 can cover the smell.
But, as the number of zombies rise, the living residents of his home-town of Springdale go from curious to hostile. The behaviour of the living horrify the zombies! This leads Archie to consider going from a convener of a support group to poltical activist.