Have you made sure app syncing is turned on?
With your iPad plugged in, select it in iTunes under the devices list. Go to the Apps tab at the top and make sure you have Sync Apps turned on. Also make sure the apps you want to sync have checkmarks next to them in the list. Both are needed to get them to sync to the device.
Other things to check: make sure the computer is authorized under the Store menu, and that you are logged into your account. It should show your Apple ID (email address) in the top right corner of the iTunes store. This needs to be the same account as the one the iPad is associated with.