Buy apps in the iTunes Store. Click the App Store link on the main Store page. After you've shopped, connect the Touch, and sync'em up. Chapter 5 explains the fine art of syncing.
Buy apps on the Touch. When you've got a Wi-Fi connection, tap the blue App Store icon on the Home screen and browse away. At the top of the App Store screen, you can tap to see the Top Paid and Top Free programs. At the bottom of the screen, you can find apps grouped under Featured, in Categories, or by the Top 25 apps in the Store. A Search icon ( ) awaits if you're looking for something specific. When you find an app you want, tap the price icon; it turns into a Buy Now button. Hit that, type in your iTunes Store name and password (even if it's a free application), and the download begins. After the program has finished loading on the Home screen, tap the new icon to launch your new app and start using it.