So I'm completely new to electrical design. I thought I'd try out the most basic experiment I could think of. Here I hooked up two AA batteries to a breadboard along with a 10 K resistor. When I attempt to measure the voltage drop across the resistor by touching the leads to both ends I get an output of .1 V. If I understand correctly the output should be about 3 V. Is there something I'm doing wrong? Here's a picture of my set up.
Based on this clearer photo I found of your meter:
You have it set to the 1.5V battery tester mode. You need to set it to the voltage measurement mode, as others have pointed out. The DC voltage range is at the top, going between 2 and 600 volts. You need to choose the next range higher than the expected voltage. In your case, you're expecting 3V and the next highest range is 20. Set it to the 20V setting and I think you'll see what you expect.