If you're looking for a simple and easy-to-follow introduction to iPhone 4's new backgrounding abilities, head on over to Oliver Drobnik's weblog and check out his latest write-up. You'll find a lovingly crafted graphic that walks you through the iPhone application lifecycle, showing how an application reacts to system changes like incoming phone calls or users' home button presses. A small portion of the chart appears at the top of this post.
Don't miss Drobnik's write-up in addition to his flowchart. I like the case he lays out for using applicationDidEnterBackground as the perfect place for saving state before giving up application control. As he points out, applicationWillTerminate will not get called in many application suspension cases.
Drobnik continues to refine his write-up, so keep checking back in for last-minute tuning and updates.