I'm running iTunes 10 on Windows7. How do I tell iTunes to download the latest episodes of the podcasts in my library and then transfer them to my iPhone.
Instead of downloading individual podcasts locate the podcast within the iTunes store and select subscribe. New episodes will be downloaded automatically. By default when you sync your iPhone with iTunes podcasts that haven't been listened to/viewed will be synced to the device.
AFAIK there's no difference between Podcasts subscribed through the iTunes-Store and manually added Podcasts. Both will reference the original feed. The store is not involved any more after a podcast is subscribed to.
I don't have an iTunes on Windows, but i guess the settings are quite the same: Open Podcasts. On the bottom of the page there's a button "Settings" and another window will open:
There's a setting "When new episodes are available". Set this to "Download most recent one" or "Download all".
After that, connect your iPhone, select your iPhone in the sidebar and go to the "Podcasts" tab. There, activate "Sync Podcasts", select those you want on your iPhone and set "Automatically include all" (or "recent ones")