Hi and welcome to iMore.
Let's see what we can do to help you. I see my iPad does this sometimes and it's usually when there is no wifi connection available. The App will just sit on 'installing' or 'updating' for ages and not do anything.
Check to make sure that you have a good wifi or cellular connection firstly.
You say you have iOS7. Do you have the latest version, which is iOS 7.1.1? If not, update and it might get rid of this issue. Is your phone jailbroken at all?
If there are other apps in the process of being updated then the install of this app might be halted for a time.
You could try a 'soft reset' by holding down the power button and the home button at the same time until the Apple logo appears and see if that helps rectify the problem. Lastly, a backup and restore might help. If none of these work then it may be a hardware issue.