To activate a cell phone with a SIM card, remove the current SIM card from the device, and replace it with a different one provided by the phone carrier. Call the carrier's customer service number using the actual phone, and request a new line of service.
There are two types of cell phones, and some of them do not have SIM cards. A cell phone that does not have a SIM card, known as CDMA phone, requires a different activation method than a GSM phone that does require the SIM. Find the phone carrier, and either call customer service or visit one of the carrier's retail locations. After you contact the carrier, give them the 18-digit serial number that is located on the battery of the phone, along with any other information needed to activate the phone. This enables you to initiate a new line of service under your own name.
Cell phones that do not have SIM cards don't always have to be activated by the same carrier that was previously used. Contact the cell phone carrier that you are interested in using, and ask if they can reprogram the device to work under their network, which is often possible.