how do I measure the glass on a patio door (glass replacement)
The glass is held into the frame in different ways depending on the manufacturer. To properly measure the entire frame should be disassembled. The glass must be ordered to size and manufactured, as it must be tempered glass, tempered glass cannot be cut once made.The material that holds the glass (rubber or vinyl channel usually) will likely need to be replaced as well. This can be very complicated for modern units with dual-pane glass (there is also the process of filling the interstitial space between panes with inert gas.)  

Is contractor you are hiring specifically qualified for this work? He should be the one to measure and order the glass, and would be responsible for errors.

You should be made aware that it is much more common, and probably less expensive, to install an entire new door and frame assembly. They even have units designed to retro-fit without removing the existing metal frame, thus avoiding plaster/stucco work. I would call a licensed and well known window and door installer in your area.