Your first encounter with GIT as a version control tool may be quite intimidating, especially if all you had been using so far was something simpler like Subversion, TFS or, God forbid, Visual Source Safe. "Version Control with GIT" by Jon Loeliger, Matthew McCullough (published by O'Reilly) leads you on a journey to become a master of the tool. But the path is not short and easy. If you need quick gratification, then you might have to look elsewhere.
Do I Need a Book on GIT?
There a plenty of GIT related resources online, and more get added the more it is adopted even outside of the open source world. If your use of GIT is just only to share your own pet projects on GitHub or to occasionally fork an open source repository, make a few changes and submit a pull request, then probably a brief list of commands with some basic concepts will get you covered.
On the other hand, if to use GIT on a daily basis at work, or work on a complex open source project with dozens of contributors and hundreds of commits, then you need to go a bit deeper and understand the nuts and bolts.
What's In The Book
After touching briefly on the installation process, the first dozen of chapters deal exclusively with one (local) repository: the object model, the index file, commits, branches, diffs and the all important concept of merging. Sometimes the description is so accurate that you can almost visualize the software data structures underlying the design concepts the author is guiding you through; but this is not just a technical curiosity to entertain the reader: everything that is discussed has got practical implications on your usage of the tool (e.g. which merge algorithm you should choose, or whether to opt for a 'rebase' versus a 'cherry-pick').
The book then devotes a couple of chapters covering how to interact with remote repositories, and then tackles more advanced topics like repository management, patching, hooks, submodules, interacting with SVN and a few other tip and tricks. It finally mentions GitHub in the last chapter.
The Good and the Bad
If you need detailed information about GIT, then this is the deal (short of reading the source code I guess). Every aspect of the tool is explained (sometimes in excruciating detail) and the authors go to a great length to provide tips and gotchas on commands (especially when you might easily shoot yourself in the foot). However this is not a quick read and it will take time to digest it.
What's missing, maybe, it's a 'quick start' chapter at the beginning to get you going if you need to be up and running in a short amount of time (say you have landed a new job where GIT is in use and you have little or no experience). That would help with the transition while giving you more time to go through the details. Unfortunately, the reader will have to look for such a compendium elsewhere.