Summarize:

You should only use an unlocking service if your carrier refuses to unlock your phone. Reputable services include "Free Unlocks" and "CellServices (around $20), as well as UnlockBase (around $10). This menu contains information about your carrier (e.g., Verizon or Sprint), your phone model number, and your IMEI number. The unlock service will need this International Mobile Equipment Identity (IMEI) number in order to issue a code to you. The unlock service should not ask you for personal information such as your home address. You may have to enter your phone number and name as it appears on your contract. Most unlocking services support PayPal--your most secure option--in addition to standard Visa cards. If you want to use PayPal but don't have an account, set one up for this transaction. Most services will send you your code within an hour, though some take as long as three business days. Most unlock services will tell you approximately how long you'll be waiting for the unlock code on their website. You will need to enter this number into your phone after installing a new SIM. To activate the unlock code input, you'll need to replace the current SIM. You can find SIM cards at their respective carrier stores (e.g., a Sprint SIM card would come from a Sprint store). Turning off your phone will prevent the SIM card from being damaged when you remove it. It should be located on the side of your phone, on the same side as the Power button. The SIM card tray should slide out. Your card removal tool should have come with your phone, but you can also (gently) use a bent paper clip for this step. Your service provider can also open your SIM slot for you. Set it aside in a safe place, such as a plastic bag. It should only fit one way, with the gold strips pointing down (away from the screen side of the phone). This should turn your phone back on. Your phone may reboot after this point. If you switched from AT&T to Verizon, for example, the service provider name in the information bar at the top of your screen should say "Verizon" instead of "AT&T".
Ask your carrier if your phone is eligible for a free unlock. Search for "HTC phone unlocking service". Open your "Settings" menu. Select the "About Phone" tab, then open "Phone Identity". Scroll down to find your IMEI number, then write it down. Enter your IMEI number and email address into the unlock service's site. Purchase your code using a secure payment method. Check your email for an unlock code. When you receive your unlock code, write it down. Purchase a SIM card for your new network. Hold down the power button, then select the "power down" option. Find the SIM card access slot. Insert your card removal tool into the hole next to the slot. Remove the old SIM card from the tray. Insert your new SIM card into the tray. Hold down the power button. If you have a SIM pin number, enter it now. Enter your unlock code. Confirm that your unlock was successful.