Hello Hashappendbefore,
This is a very common problem that should be able to be fixed very quickly.
I have a few easy steps for you to follow that should resolve the issue.
1)Check your network connection. You could be having connection issues.
2)Even if your network connection seems okay, try switching to Cellular and try connecting to the App Store.
3)If this doesn't work, turn your iPhone off, wait a minute, and turn it back on. Repeat the above steps.
These simple steps should fix your problem. If not, contact an Apple Specialist.