I need to be able to contribute to a relatively large Adobe AIR project and I'm starting from scratch with this technology. What's the best way to go about it?
I usually get a good book/tutorial and work my way through it but this time it seems there's just too much to learn for this to be feasible within a reasonable time frame. I would need books on Actionscript, FLEX, etc...
Do you know of any good resources that might be useful for this particular case?
How would you go about it if you were in my shoes?
On your own? I'd look for a reasonably simple project on github, or somewhere the source is available. Before you start trying to understand everything, prime your brain with a little previous exposure. Look through the directory structure, look through the source code. See if anything makes sense. Build it, to understand the build process. Run it. Now change something. Could be a title bar, a background image, a validation. Just something. Build it. Check your work.
Now your head is in the right space to learn. Find a cheat sheet, and go through that. Go back to the app you're fiddling with and walk through it again with the cheat sheet handy. Change something more fundamental. Build. Check.
After you've gotten the cheat sheet (primer) understood, build something from scratch. As run4yourlives mentioned, the blog is the new hello world. Build that, build a file uploader, and build something event-driven and flashy. At this point, you'll want to go through a book -- but skim the whole book first to get a sense of where things are.
Now dive deep. As you are learning, write stuff down -- build a tutorial. Try to explain it to someone else (that always helps me, anyhow). By the time you finish writing your tutorial, you'll be ready to contribute, and you'll learn more on the job.
Good luck!