Your cell phone plan may charge you fees if you don’t have a plan with them that allows calls outside the US.  Call your provider and tell them what your plans are – you are visiting for 1 week, you plan to stay for 6 months, etc – and they will give you your options.

If you don’t have a plan to call outside the US, before you depart from the airport to Mexico, turn your phone to ‘Airplane Mode’ and this will prevent you from connecting to your service plan.  You can still connect to WiFi while Airplane Mode is ON, so you can use your phone to take photos and make calls/connect to the internet through a WiFi connection.