I bought a couple of older bikes (early 80's maybe) and am not sure what size the rims are. How do you measure them?

Measure the diameter of the rim. Wheels are specified by their "bead seat diameter", which is where the tire bead seats inside the rim. The actual rim sidewall extends about 4-5mm above the bead. So, a 700c rim, which has a bead seat diameter of 622mm, has an actual rim diameter of 630-630mm. See Sheldon Brown's article on tires (http://sheldonbrown.com/tire-sizing.html) for other common wheel bead seat diameters.