With nearly every exercise, performing a unilateral (1 arm / 1 leg) version brings the core muscles into play a lot more.
With an exercise like the chest press, performing the exercise 1 arm at a time means the weight tries to rotate the body. The role of the core in this instance is to prevent that - known as anti-rotation.
It's an important way to strengthen the core muscles which has a lot of carry over to sports and other exercises.
So not only are you working the chest, shoulders and triceps, you are getting a lot of core muscles fired up too.
-Adjust seat height so lower handles are at or slightly below chest height. Tall people may need upper handles for comfort.
-Hold one handle at width that allows wrist to be straight, do not allow hand to bend back either
-Sit with back firmly against back rest and squeeze shoulders back and down. Should feel back muscles tighten. Brace abdominals and take a deep breath in.
-Breathe out hard and press handle away from body until arm is extended.
-Lower handle back towards body as breathing in. Stop once elbow is roughly in line with body (do not allow weights to rest) and repeat.
-Complete all reps with one arm before switching sides
This is my, mostly, Personal Trainer musings and information which I hope you'll find helpful!