Call Your Wireless Provider and Ask for the Network Unlock Code:
Most will provide you with one and some even do it for free if your contract is up. Current laws require carriers to provide the Unlock Code after 6 months of continuous ownership. Once you're provided with the code you should be able to enter it into your phone to remove the lock.  Most carriers will send you the code via Text. This is the easiest and most common method of unlocking. Your wireless carrier may be able to unlock the handset remotely. Make sure your phone actually needs unlocking by inserting a SIM card from another network into your mobile phone. If it's locked, a message will appear on your home screen.

Try an Unlocking Web Site:
There are websites that offer to create the Unlock codes for you, but read reviews and take a view on how trustworthy they are before you hand over any money. It may be worth more, but this service shouldn't cost you more than a few dollars.

Visit a Wireless Repair Store:
Cellular repair shops that are not affiliated with a single wireless carrier can usually unlock your phone. Because they do all the work, expect to pay more than an unlocking web site.

Technical Forums:
There are few online discussion forums with members who are willing to help you for little or no fee. Forums that focus on your specific model of phone are the most helpful including those based outside the US.

Do It Yourself:
If you're technically-minded you may be able to do this yourself but it's not very easy and you will need special software.