Tap Settings > General > About
Scroll down to locate the listing for Carrier Lock
You want to see a message there of No SIM Restrictions
If you see Carrier Lock or SIM Lock, you need to contact your carrier and ask them to remove the lock on the phone. They will do this if you have met the terms of your original agreement with the carrier and your account is in good standing
Only the carrier can unlock the phone. Apple cannot do this, so Apple is not involved at all in this process.
Once the phone is unlocked, you can contact and set up service with a carrier of your choice assuming that you will be paying the bills. If someone else will be paying the bills, they will need to contact the carrier that they want to use to set up service for a new account.