The only way you can change from one carrier to the other for your iPhone services is if you are able to unlock your iPhone. Some carriers offer this service if you meet particular requirements and some do not, so you will need to call your carrier or the carrier you are interested in to find out what the available options for you.
If you are able to have your iPhone unlocked to switch carriers, you will have to have a SIM card from the carrier you are going to sign up with, so you may need to take your iPhone in to have this new SIM card installed or you can eject the old SIM card and put the new one in by yourself and walk through the setup process that will come along with the SIM card.
If you don’t have another SIM card to use, but know you can switch to a new carrier then you will need to back up your iPhone and erase all data. When you have finished doing that, complete the setup assistant through iTunes and restore your backup.