Just like AirPlay, AirPrint is a flagship feature of iOS 4.2 that initially offered more functionality than Apple finally delivered, yet despite arriving without network printing support, if you have one of the few supported HP printers it does indeed feel like the future.
AirPrint is a system-wide service available in built-in Apple apps like Safari or Photo, App Store apps like iWork's Pages, and 3rd party Apps that have enabled support. Like any new feature, more and more apps will add that support as they push updates through the store.
To use AirPrint simply tap the appropriate button -- the "arrow coming out of the square" Action Button in most cases -- and then select your AirPrint compatible printer from the list (if you haven't selected it previously). Choose how many copies you want and hit Print.
Once the print job has started you can double click the Home Button to reveal the Fast App Switcher interface and the new Print service that will pop in there. Tap it and you'll get a snapshot of what's going on with your print job, including the ability to cancel it.
Right now, the current list of supported printers is sparse:
More models from more manufacturers will no doubt be hitting the market eventually, and hopefully Apple will iron out whatever bugs or kinks were affecting AirPrint on networks and restore that feature in an upcoming software update. (If you're the adventurous sort who doesn't mind tracking down files and hacking in Command Line or Terminal, we have tips up on how to re-enable network AirPrint for both Windows and Mac.)
Have you tried AirPrint yet? If so let us know how it worked for you and what, if any, features you'd like to see Apple add to it in the future!