Place the iPod in recovery mode using one of these programs and then restore via iTunes:
For MAC or PC
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 backup of the iOS device that iTunes makes.
You can redownload iTunes purchases by: