How to redownload iTunes Apps
"I did a restore on my iPad and lost all my apps. When I go back to the iTunes App store it says that I have to buy the same iTunes apps I already purchased. How can I redownload my iTunes apps that were previously purchased from the iTunes store?"
The iTunes App store assumes you will sync your apps with your computer when you connect your iPad. What they don't do is make that process automatic by enabling app sync by default. This translates to a situation like yours, where you purchased a bunch of iTunes apps, restored your iPad, and then realized you didn't have any of your apps. Fortunately, there's a solution that will get you the apps you previously purchased, without spending any additional money.
Possibly the most annoying aspect of getting all your iTunes apps redownloaded is the fact that there's currently no download all setting. You have to recover them one at a time. This relies on you remembering which apps you downloaded or reviewing the purchase history in your account to see the list of purchases you made over time. If you have lots of apps, that purchase history is going to become your best friend in terms of finding all the missing apps.
iTunes Won't Charge for a Previously Purchased app
While it isn't obvious, the way you redownload iTunes apps is to go to the iTunes store and click on the buy link for each app. This will warn you that you will be charged, but that's only because the software isn't smart enough to know you made the purchase until after it sends the buy request to the store. You won't be double charged. I've tested this on multiple apps in my own account to verify. You will see an image like the one below warning you of the charge, but don't worry, it won't actually charge you.
You need to click the Buy button to get your app back. Once you click that buy button, you will see a second message saying You have already purchased this item. Clicking OK will complete the process and start the download.
I recommend doing the re-downloads on your computer so that you have a backup of all your apps. As I said before, if you have a large number of purchases this will take awhile and you won't want to go through it again in the future.