It's not clear from your post what characteristic of your stem that you want to measure.
First there are two general types:
-quill stems
and
-threadless AKA aheadset stems

For quills you can have:
-different quill diameters
-different height (or length of the part that gets inserted into the steerer)
-different handlebar clamp diameter
-different forward protrusion, sometimes called neck or length
-different angle between quill and neck

For a threadless stem you can have:
-different steerer tube diameters
-different handlebar clamp diameters
-different forward protrusion
-different angle between steerer tube and stem forward extension
-of less concern, but still there, threadless stems can have different amounts of build height, the amount of room they take up on the steerer tube. Replacing one stem with another may require a change in spacers to be able to set the preload.

The diameters are most easily measured using a vernier caliper. Particularly for older road bikes and some Schwinns, you do need to get the tenths of millimeters right.

Forward extension is measured center-to-center. Angle is a bit tricky, but there are drawing tools and workshop tools to be had for the job.