Did you make sure you're signed into the App Store, as I described above?
What have you tried to do to resolve the problem?
Do you get any error messages?
Go to Settings > General > About for the following info: What model of iPod Touch? What version of iOS? How much available storage?
Are you connected to wifi, and can you view web pages?
You can try each of the following, one at a time, testing the App Store again after each item.
Sign out of iTunes & App Store and then sign back in (Go to Settings > iTunes & App Store, tap on your Apple ID, select Sign Out from the menu that appears)
Force-quit App Store (exactly how depends on your version of iOS) and power-off/power-on iPod
Make sure you have a backup of your iPod (either in iTunes or iCloud), then reset the iPod (hold power and home buttons until the Apple logo appears)
If none of that works, restore your iPod to factory settings, following this support article:
https://support.apple.com/HT204686