I am trying to design a cad model that snaps onto the sides of the eye things on the gas mask, but I don't know how to measure it in order to represent it geometrically.

I would first recommend you search for a CAD model online for the same product or search for its standard dimension. if you didn't find any, you could use many tools to measure it accurately, for example by using a digital caliper, or for greater details you can use a digital microscope for more accurate dimensions( but I don't think this case requires this accuracy), so I greatly recommend using a digital caliper and measure the key dimensions that mainly effect you design purpose. Remember a good product requires a try and error procedure. 

good luck traysonc!