This question is about an iPod touch, correct? It's sort of like adding songs...
Select iTunes Store (under STORE) in the iTunes sidebar (left side of window). Click on App Store in the bar that goes across top of window. Find and download an app you want (some are free and some you buy).
Select Apps (under LIBRARY) in the iTunes sidebar, to confirm that app is now there, in your library.
Select your iPod touch (under DEVICES) in the iTunes sidebar. Over to the right, go to the Apps tab. Find the app that you downloaded on the list, and select it for syncing. You can organize where the app will go, or do that on the iPod touch. Click the Sync button.
Alternately, you can use the App Store app on the iPod touch, and download apps directly from your iPod touch (without using iTunes on the computer and then syncing).