Way 1. Ask for Help from Carrier
First of all, you should be aware of whether your carrier offers unlocking or not. Some popular carriers in USA, like AT&T, T-Mobile, Verizon can assist you to unlock your iPhone if you have an eligible device meeting all requirements. >> Check Widewide iPhone Carrier Support and Features
Steps: 1. Follow the instruction given by your carrier to ask for an iPhone unlock. Some need you to fill a request form. Some may require you to download official unlock app. When your request is confirmed, your carrier will unlock your iPhone directly or send you an unlock number. If you get nothing several days later, contact your carrier again.
2. Once your iPhone is unlocked, remove the original SIM card and insert the new one. After that, set up your iPhone again. If you haven't gotten a new SIM card right now, you should backup iPhone and then reset to erase all content and settings of your iPhone. Later, restore iPhone from backup.
Way 2. Try IMEI Unlock
How to use IMEI unlock? At the beginning, you should know your iPhone IMEI number. There are many ways to find this number.
The next step is to find a reliable IMEI unlock service. You can search iPhone IMEI unlock on ebay and pick out one referring to ratings, sales and reviews. And, iPhoneIMEI.net is recognized as one of the fastest and most effective unlocking methods.