The following four steps can be accomplished without a plastic opening tool. However, it's recommended to use a tool to best avoid breaking any clips along the perimeter of the rear case.
Insert a plastic opening tool or fingernail into the notch in the gap between the rear case and the rest of the phone, located at the top of the device.
Gently twist the opening tool to disconnect the clips securing the top of the rear case.
My Samsung Galaxy S III does not seem to have a sim card. I bought it through Sprint around 2011 time frame. Do you know if it has an internal sim card that can not be replaced?