It has always been common for volunteers to share proofing work among themselves--you take the first five chapters, I'll take the next, and so on.
When you're just starting as a PG volunteer, you should go to one of the Distributed Proofing sites [B.4] and do some work there to get a grounding in the basics and a feel for whether you would like to continue working in PG. In distributed proofing, you get a very short section, as little as a page of text at a time, and usually an image file of the page as it scanned. You then make the text match the image. This is a great start, since all you have to do is read, compare and correct. However, other work also needs to be done, and will normally be done by the project managers of these sites. The samples below give you an idea of the whole process, and also some ideas of what proofing a whole book from start to finish is like.