The best advice we have for you is to do your update with iTunes after doing a full backup first. This is the safest method of doing iOS updates and is least prone to issues.
If you have your heart set on doing the update on your phone, first make sure you have wifi and your phone is fully charged. If you were unable to download the full update perhaps you lost internet connectivity.
Do a full restart by holding down Home and Power buttons for 10 seconds then allow the phone to restart and try again.