First, try a system reset. It cures many ills and it's quick, easy and harmless...
Hold down the on/off switch and the Home button simultaneously until the screen blacks out or you see the Apple logo. Ignore the "Slide to power off" text if it appears. You will not lose any apps, data, music, movies, settings, etc.
If the Reset doesn't work, try a Restore. Note that it's nowhere near as quick as a Reset. From iTunes, select the iPad/iPod and then select the Summary tab. Follow directions for Restore and be sure to say "yes" to the backup. You will be warned that all data (apps, music, movies, etc.) will be erased but, as the Restore finishes, you will be asked if you wish the contents of the backup to be copied to the iPad/iPod. Again, say "yes."
If you restore from backup the app data will be like it was when the backup was made:
To restore from backup see:
If you restore from iCloud backup the apps will be automatically downloaded. If you restore from iTunes backup the apps and music have to be in the iTunes library since synced media like apps and music are not included in the backup of the iOS device that iTunes makes.
You can redownload most iTunes purchases by:
Restoring to factory settings/new iPod erases the iPod. reinstalling apps does not restore app data except for those apps that sotre info on servers.