How to Download an iPad App from the iTunes Store
When you find an app you want to try while browsing the App Store on your computer, just click the app’s Free App or Buy App button. When you do so, you have to log on to your iTunes Store account, even if the app is free.
After you log on, the app begins downloading. When it’s finished, it appears in the Apps section of your iTunes Library.
If an app costs money, you’ll get a receipt for it via e-mail, usually within 24 hours.
Downloading an app to your iTunes Library is only the first half of getting it onto your iPad. After you download an app, you can sync your iPad so the app will be available on it. You can also get the app via the App Store’s Purchased tab or by enabling automatic downloads on the Settings app’s Store pane or the iTunes Preferences Store tab on your computer.
If you want apps to download to your iPad automatically, regardless of which device you used to purchase the app, you can set that up:
On a computer: Connect your iPad via either USB cable or Wi-Fi. Launch iTunes and click the iPad button near the upper-right corner of the iTunes window, or click your iPad’s name in the sidebar on the left. Click the Apps tab and enable the Automatically Sync New Apps check box.
On your iPad: Tap Settings→Store. Then turn on the switch for Apps in the Automatic Downloads section.
You can enable Automatic Downloads for Music and Books on your iPad (but not in iTunes).
By the way, if your iTunes App library doesn’t look like ours (with big icons in a grid pattern), you’ve probably clicked the List tab; the All, iPhone/iPod touch, iPad, and Updates tabs display icons as shown.