Summarize the following:
Go to Settings, select Security and Privacy, and then SIM Card. Scroll down and tap the Unlock Phone button. Enter your code and tap OK.  You have 10 tries to enter your code or your phone will be disabled. First, disable all network connection. You can see your connections by opening the Manage Connections. Make sure that your WiFi and mobile networks are disabled.  Open the SIM Card menu by opening Options, selecting Device, Advanced System Settings, and then clicking SIM Card. Type “MEPD” while in the SIM Card menu. A new menu will appear after you finish typing, and Network should show as Active. 71xx, 81xx, and 91xx model users will need to type “MEPPD”. Type in “MEP[Alt]2”. If nothing happens, try typing “MEP[Alt]4”. You need to press the Alt key to enable typing numbers. 71xx, 81xx, and 91xx model users will need to type “MEPP[Alt]2” or “MEPP[Alt]4”. Enter your unlock (MEP) code. You have 255 tries to get it right, so don’t mess it up! Once you’ve unlocked the phone, you can insert your new SIM card and re-enable your network connections. Remove the existing SIM card by removing the battery and popping the SIM card out of its housing. Insert the SIM card for the new network. When you power the phone back on, you will be prompted to enter your unlock code.

Summary:
Unlock BlackBerry 10 devices. Unlock BlackBerry 7 devices. Unlock BlackBerry 6 devices and earlier.