Here's an easy, sure fire method to tell what eye dominance any other person has in seconds.
Watched a hunting firearms instructor perform this on 25+ students in a class where he absolutely identified each persons eye dominance within 5 seconds each - he did the entire class in about 2 minutes.
He had everybody stand up and face him at about a 20' distance. He had everybody point one arm straight out with their finger pointing straight at his nose, with both their eyes open. As they did this, he looked at their eyes. What is seen is one eye looking straight at his (the testers) eyes, and the other eye is sort of looking off in a slightly different direction. Whichever eye is looking straight into his eyes was the persons dominant eye.
It absolutely works, every time. It's actually kinda' funny to see this! Try it yourself with friends. One nice thing about this method is the tester determines which eye is dominant, not the student. I've corrected numerous people who believed their dominant eye was the opposite of what was factual...
Every so often you'll find a person who has both eyes looking straight at you, or equal dominance. This is THE WORST condition to have, because neither eye is truly dominant, or can sometimes be so slight a difference that either eye can capture dominance. When clay bird shotgunning where both eyes should remain open (best choice) this truly sucks as the angle change can really throw off the point (notice I said point, not aim).