Connect the iOS device to your computer and restore via iTunes. Place the iPod in Recovery Mode if necessary to allow the restore.
If recovery mode does not work try DFU mode.
For how to restore:
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 iPod backup that iTunes makes.
You can redownload iTunes purchases by: