Ars Technica's iPhone wonder woman, Erica Sadun, has put together what must be the first expert level how-to: Pushing tweets to your iPhone with Apple Push notifications
Ars shows you how to create a Push-based Twitter update notification system for the iPhone without actually showing you any of the details due to the ongoing NDA. (But don't worry, we tell you exactly where to find the instructions.)
Now if you need help getting your code on, it just so happens that the Stanford iPhone Application Development course (the one being offered via iTunes U) looks like it has "make your own Twitter client" on the agenda.
Ready? Set? Push Tweet!