Depth can be measured by inserting the depth rod into the hole you are measuring. When you adjust the jaws using the thumb screw, the rod will protrude from the end of the caliper.
When taking measurements, try not to touch the measuring faces of the caliper. Even the smallest amount of oil on your hands can affect the accuracy of your readings. Want to learn more about calipers? Go to What is a Vernier Caliper?