How do I download iPhone apps from the Apple iTunes store

You aren't the first person to encounter this problem: I did too. The problem is that you appear to have diverged from the default configuration and so you now need to go into your preferences and tweak it to let you see the app store in iTunes. It's there (well, access to it is there) you just aren't showing it.
When I first started poking around, I figured that it'd just be a new category in the iTunes Store, actually, y'know, like podcasts and audiobooks, but it's not (rather confusingly, if you ask me, since in so many other areas the app store is functionally identical to the music store).
Start up iTunes 7.7 or newer and you're probably seeing something like this: