Q: How do I get a Genius Mix from iTunes onto my iPhone 4?
A: You must be using automatic synchronization in order to transfer Genius Mixes to your iPod or iPhone; transferring Genius Mixes when managing your content manually is not possible. If you are using automatic synchronization and have Genius Mixes present in your iTunes library they should simply appear as special playlists for synchronization on your Music settings screen.
Connect your iPhone 4 to your computer, select it in the iTunes Devices list and choose “Music” from the options at the top of the screen. Your Genius Mixes should appear in their own folder above your playlists and can be selected in the same manner as any other playlist.
If you don’t see any Genius Mixes listed here, be sure that iTunes has actually created some Genius Mixes in your library by looking for the “Genius Mixes” option on the left-hand side of the iTunes window. If you’re not seeing any Genius Mixes in your library at all, try selecting Update Genius from the Store menu in iTunes which will refresh your Genius data and create new Genius Mixes if possible.