How do I delete an app and re-download?

Delete the application from your device. Press down on the icon until all your icons start shaking. An X should appear on the top corner of the icon. Press the X, and you will be prompted to delete.
Re-download the application with the same iTunes login, and you will not have to purchase it again. See:
Please restart your device after re-downloading. See the “restart” section below:
iPod touch:
Android powered devices