After learning the alphabet, this is the best place to start. This book assumes you know next to nothing about Arabic grammar and walks you through complex concepts using lots of examples, drills and charts. Unlike most other Arabic grammars, this book was written with students, not scholars, in mind. Many of the explanations are informal, and some are humorous. Overall, the author strikes a palatable blend of substance and style. Most of the book is dedicated to conjugation and the verbal measures. But it contains lessons ranging from simple conditional constructs to those rare rules even educated natives forget. Unfortunately, this book was never made available to the general public. I think it was originally published for university graduate students and then later for military students. However, from time to time, copies do crop up on eBay.
If you prefer an oldschool, no-frills, dry-as-toast, kick-in-the-nuts presentation of grammar, then try to get your mitts on this beast: Grammatical Notes from DLI c1970s (thumbnail on the right). Many of the DLIFLC books were written specifically for military linguists. The pace of these books is a lot faster. This doesn't necessarily mean better, but if you want to see how the pro's do it, then keep an eye out for oldies like this one.