The process is contact your network supplier .
Ask IF they offer unlocking.
IF yes request the unlock and pay any fees requested.
Your network supplier then contacts Apple to request the White listing (Unlocking) of your phone on the iTunes servers.
Apple do this -It takes anything from 3 days to several weeks to complete.
On completion Apple confirms this back to your Network supplier (NOT YOU)
Your network supplier contacts you via email or SMS inviting you to connect your iPhone with your computer via the supplied USB cable and launch iTunes and follow on screen prompts through to the "Congratulations your iPhone is now unlocked" screen.
All these steps need to be carried out with the ORIGINAL SIM and by REGISTERED account holder used when setting up the phone.
Once the Congats...... screen has been reached you can swap out the REGISTERED SIM and replace with a compatable SIM on another network.
Only the original SIM and Account holder can initiate an unlock- If you bought the phone used/second hand you CAN NOT UNLOCK through official routes
Once unlocked use of a Mobile Virtual Network SIM may result in difficulties sending SMS messages.
You may have to go into Setting /Network/Cellular/Cellular Data Network and enter the correct settings manually.
Further caveat Cellular Data Network menu is SIM card dependant if its not supported you CAN NOT change the settings manually then you may need to contact the SIM card company - They can send a setup SMS if they support this process.