To make sure app sync automatically:
If you are in the U.S. then download iTunes 10.3 and make sure your iPad is running 4.3.3. In iTunes go to Preferences > Store and make sure Apps is turned on. Turn the music or books on as desired. On the iPad go to Settings > Store and do the same. From that point on any app you download on the iPad or iTunes will automatically download on the other. Only works for new apps.
Otherwise:
Connect the iPad to the computer and select if from the Device list in iTunes. Go to the Apps page. Make sure you are set to sync apps, choose the selected apps by preference. Below the list of apps there is another checkbox that says sync new apps (or something like), check that too. Now, go through all the apps in the list and make sure the ones you want on the iPad are checked. If they are not, they will be removed the next time you sync, and you will lose any files or settings that you had in them.
When you are sure you have it the way you want, sync. From now on new apps purchased on the iPad will by copied to iTunes whenever you sync, and vice versa.