Your new carrier may require some steps as well
In some instances, you may need to program your phone to work with another carrier after you unlock it. For example, to program a Verizon non-iPhone Global Ready 3G phone to work with a different carrier, you'll need to use either the code 000000 or the code 123456. Check with the carrier you're leaving and the carrier you're moving to for details.
For more information
There's plenty of information online about the ins and outs of unlocking your phone. The FCC's page Cell Phone Unlocking FAQs is a great place to start. Also worthwhile is the FCC's encyclopedia entry for cell phone unlocking.
If you enjoy weeding through legalese and want the full story on unlocking, head to the unlocking guidelines set by CTIA - The Wireless Association for the guidelines that service providers follow.
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