Perform drills and games that involve catching and throwing an object. An easy test is to have two people stand directly opposite each other at a distance and toss a tennis ball back and forth, stepping farther apart on each throw. Your ability to catch the ball and throw it accurately will be a good measure of your hand-eye coordination. To increase the difficulty, increase the speed of the throws.
Play video games. While your eyes are fixated on the screen, your hands are controlling the game through a joystick, keyboard or controller. Test your hand-eye coordination by accurately maneuvering through the game and processing the images on screen with split-second decisions with your fingers.
Take online hand-eye coordination tests such as those offered at the SportsEyeSite website. Certain online applications are designed to test the difference between what you see on the screen with how quickly you respond with your fingers using the keys or mouse. Other applications are meant to test your ability to distinguish between different objects and pick the correct one.