No matter how I explain it, nothing beats the following: Grab a baseball bat or a ball-golf club and swing it just regular handed. Now if you're a terrible baseball player or golfer, maybe you can shoot a hockey shot or swing a tennis racket or even a traditional bowling shot? We want some motion that you're used to doing with your regular hand, specifically that involves bracing your weight against your instep of your plant foot.
We want a reference to feel so that we can then replicate that feeling using your non-dominant hand. When I was trying to work this out, swinging a club opposite handed hadn't dawned on me, and I regularly had the thought, "If there was just some kind of machine that I could get inside of that would put me in the right positions!"
We don't have one of those just yet.
But, the beauty of having a reference for your regular hand swing, is that you can flip it over and practice it opposite handed - which is what the bracing motion is for a backhand. You want to develop your opposite handed swing until you're nearly as proficient with taking those swings.
What it teaches you is how to keep your center of balance inside the brace of your plant foot and hopefully the instep of your plant foot as well.
Link for mobile users: Youtube
So enjoy learning to hit opposite handed... just remember that if you're working this out in the house because it's cold outside to move your wife's favorite lamp before you start!
Lesson learned the hard way.