iTunes: In iTunes, visit the iTunes Store and then locate the Purchased link in the Quick Links sidebar on the right side. Once in the Purchased interface, you'll see Music, TV Shows, Apps, and Books tabs across the top. Click on any of them to see the content available to you.
For each category, you can choose different view and sort options (viewing music by songs or albums, for example) as well as search your content using a search box on the left side of the window. At the far right, you can choose between having iTunes display all purchases, or just those not in the respective iTunes library.
To download, click the cloud icon next to a song, album, music video (found under Music), TV show, app, or book to begin the download process. You can also download all your music or individual TV show seasons by using a Download All button.
iOS: On iOS devices, the process is much more fragmented. For music, launch the iTunes Store app, and tap the Purchased button at the bottom. From there, choose between Music and TV Shows (via a pop-up menu on the iPad or from the Purchased screen on the iPhone), and the process works similar to that on iTunes. A Recent Purchases link shows you newer content, and the interface provides a few different ways to view your stuff. As with iTunes, you can choose between All and Not On This iPhone/iPod/iPad. Use the cloud icon to download.
For apps, launch the App Store app. Tap the Purchased button (iPad) or Updates button and then the Purchased link at the top (iPhone) to see your previously download apps by download date (newest first). Here, too, you can see all apps or just those you haven't installed. And on the iPad, you can choose between viewing iPad-specific/universal apps and iPhone apps. Tap the icon to download.
For books, launch iBooks and go to the iBookstore. If you see your library when you launch iBooks, tap the Store button in the upper left corner (iPad) or upper right corner (iPhone). From there, tap the Purchased button at the bottom right of the screen and you'll see a list of all the iBookstore purchases you've made in the past. Tap to download.
Apple TV: One other advantage of the iTunes in the Cloud functionality is that the second-generation Apple TV can stream previously-purchased TV shows over the Internet, rather than making you keep them housed on a computer using Apple's Home Sharing feature or streaming them locally using AirPlay.
iTunes Match is an optional subscription service that Apple plans to roll out to customers in the U.S. by the end of October. For $25, it offers both music storage and, in some cases, music upgrades.