If you're trying to install or update Instagram and the app is stuck on "Installing," first try turning your phone off and then back on:
Press and hold the button at the top of your phone until the red slider appears
Slide the red power button to turn off your phone
Wait about 30 seconds, and then press and hold the top button again to turn your phone back on
After you restart your phone, try installing the Instagram app again. Some people have reported that syncing their phone with iTunes and reinstalling Instagram from iTunes helps with this process.
If these troubleshooting steps don't help, please contact Apple support.