You're not limited to the desktop iTunes program to redownload purchases via iCloud. You can also use a handful of iOS apps.
- To redownload music you bought at iTunes on iOS devices, use the iTunes Store app. When you've launched that, tap the More button along the bottom row. Then tap Purchase.
- Next you'll see a list of all the kinds of purchases--Music, Movies, TV Shows--you've made through the iTunes account you're using with your iOS device. Tap on your choice.
- For Music, your purchases are grouped together as All Songs or listed by artist. Tap the artist whose song or songs you want to download. If you've got only one song from that artist, you'll see the song. If you have songs from multiple albums, you'll have the option to view individual songs by tapping the All Songs button or download the album by tapping the iCloud icon (a cloud with a down-facing arrow in it) next to the album.
- For Movies, it's simply an alphabetical list.
- For TV Shows, you can choose either from All TV Episodes or individual shows. If you tap on an individual show, you'll next be able to select a season of the showing by tapping on it. When you do that, you'll see all the available episodes from that season.
- Purchases available for redownload (i.e., ones not on the device you're currently using) will have the iCloud icon next to them. Songs that are already present on your device will have a grayed-out button that reads "Downloaded" next to them.