There have been precious few books in print that have updated information on how to do GIS using open source software. One reason for this is the incredibly fast rate at which popular open source GIS packages have been updated. For example, even as mainstream users fire up QGIS 1.7.4 to do their GIS work, the hard-working members of the world-wide network of developers are working on QGIS 1.9.90 build 110 (as of today). It's entirely possible that the next major upgrade to QGIS will be version 2.0, skipping public releases of versions 1.8 and 1.9 !!!
(What? You're not using QGIS 1.7.4? Go here immediately!)
Locate Press published a book called The Geospatial Desktop: Open Source GIS & Mapping. This book is an update of an out-of-print 2008 book called Desktop GIS: Mapping the Planet with Open Source Tools. It uses more modern versions of open source tools, including QGIS, to teach readers the rudiments of GIS. It is available from Amazon.com in softcover print (US $50) and kindle (US $29) versions.
I liked the original book, so I will probably be purchasing the Kindle version. Some of you may have had a chance to look at the original as well. The author is Gary Sherman, the developer of the original versions of QGIS. His very informative blog is here.
Gary Sherman also noted in a video interview that he is working on a separate book on QGIS. If so, this will be the first published "how-to" book (I assume that's what it will be) on QGIS. (For other QGIS resources --- and there are many, many of them --- see http://www.townshipgis.com/resources/qgis.)
If you're looking to see what you can do using other, non-QGIS open source GIS tools, or if you need to brush up on GIS itself, then you might consider getting this book. I'll let you know when the QGIS book comes out.
18 April 2012 update: I left a question last week at Gary Sherman's blog, asking him about the status of his QGIS book project. He graciously responded, indicating that the project is on hold at the moment. The incredible pace of establishment of new features, functions, and plug-ins in the development version of QGIS (v. 1.9.90) guarantees that any QGIS book written now will be obsolete upon publication. The strategy is to wait until version 2.0 comes out before deciding on whether and when to re-start the QGIS book project.