Reinstalling an App that was bought is a convenient function. If you had to delete the App for space usage reasons or had to do a reset to factory settings and lost all your Apps, it is easy to recover them. Apple is very user friendly and their Web site offers guidelines to troubleshoot any problem you may experience with your iPod touch or iPhone's App problems.
How to Reinstall an App That I Bought
Sync your iPhone or iPod touch after you add every App. Connect your iPod or iPhone to your laptop. Open iTunes. Click the "Sync" button. Wait for the sync to finish.
If an App has been deleted that you have purchased from the App store, connect your iPhone or iPod touch to your computer. Open iTunes. Click on your iPhone or iPod button. Click on the "Applications" button on the task bar for your iPhone or iPod. Reference the Applications list. The Apps currently installed on your iPod or iPhone will have a check mark next to them. The Apps that you have purchased and backed up that have been removed from your iPod or iPhone will be listed under your Applications but will not be checked. Add a check mark to the Apps you wish to re-install onto your iPod or i Phone. Click the "Sync" button.
Click the "Eject" button to safely unplug the iPod or iPhone. Unplug it. Page through your iPod or iPhone pages until you find the Apps reloaded.
An alternative to the aforementioned steps is to log into the App Store. Search the App you need to reload. Click the "Install" button. Enter your password and begin the download--you will not be charged if it was previously purchased.