Looking at an early caliper, you'll notice that it kinda looks like a tomahawk and has a scale down it's length. More about the scale later. On the bottom left, the "blade of the hatchet" are the jaws of the caliper for measuring outside dimensions - think of a tube. This would measure the outside diameter. The "pike" on top of the hatchet is used for measuring inside dimensions . Again, think of a tube's inside diameter. Looking all the way to the right...I know it's hard to see...but there's a little "tail" sticking out of the center of the handle. That will measure the depth of a step or some other similar feature. That little button on the top near the "pike" is a locking screw. The one just below it is a thumb button.
Step 1: holding the caliper
This is the proper way to hold a caliper. Use your thumb to slide the jaws open and closed. Yup, another tool that was totally designed for righties. Use the locking screw at the top if you want to set a dimension on the caliper and then check parts against your setting. Though it may not look it, the measurement between the inside and outside jaws are EXACTLY the same.