Actually, the books aren't typed in. Scans are made of the pages and optical character recognition used to try to make sense of it. Depending on the age and condition of the book, this may be very good to pretty challenging.
As you might suspect from that, the major need for Project Gutenberg is not typing, but careful proofreading.
To that end, the Distributed Proofreaders at http://www.pgdp.net exist. They train and mentor and it is really kind of fun finding little things to fix. Texts are rated by difficulty and after on-line training, you start proofing easy texts as a front line proofer. Things generally go through two proofers before hitting formatting and final editing.
Everything is done through a web browser interface.
As you proof more pages, and as succeeding proofers proof your proofs (what a phrase that is), you'll develop skill in spotting things and leave less for the next round. You get feedback on what later proofers found, too. After a while you'll have a high enough score to work in the second round of proofing, or if you like get into the formatting and final preparation.
Things are fed to you one page at a time and that's all they ask--a page a day. It's kinda like Lays potato chips, though, if you have the time--can't just proof one. A page in an easy text takes a couple of minutes, in a medium to hard, rarely more than 5-10 minutes. So it isn't much of a time commitment.
It is pretty cool to see a book or magazine you worked on progress through the process. And you're working with 500+ folks any given day you log on.
Ok, enough of a commercial--can you tell I like the whole thing? 
I highly recommend going through the beginners FAQ and give it a try. I like to do a page or two in the middle of the day as a break from work.
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