Oy.. this is tough to explain.. Especially over the internet, but I'll try...
This is how I was taught to teach a horse to stand square. I'm sure there are easier ways to do it, but this is how I did it:
First things first, make sure your horse can stand still really well.. It'll be really frustrating to teach a restless horse how to stand square (trust me, I know from experience on that one.. LOL!)
Basically, you're going to teach your horse that when you pull up on the lead rope (like literally UP, toward the sky) he will move his front feet, and when you pull down on the lead rope, he will move his back feet.
The way you go about training this takes TIME.
Start by using your show halter (usually with a lead chain, not to be harsh to the horse, but to get more response from less pressure you use)...
Pull the lead rope up/down and once your horse moves the correct feet, praise him.
Say you pull upwards on the lead rope and the horse moves its front foot, then you praise him by releasing the pressure. Do the same on the back feet. Pull downward on the lead rope and once the horse even slightly moves one of its back feet, then release the pressure. It DOES NOT happen overnight. I did this for 10-15 minutes every day for almost 2 weeks before Putts understood what I was asking.
Eventually you will be able to pull upwards or downwards on the lead rope and get your horse to move its feet until they're where you want them, but don't forget to release the pressure once they've taken a step, even if it's an incorrect step. Let them set their foot down and try again after you've released the pressure. It takes a couple tries usually for a horse to get it right, but the judges are patient, and the more you do it with your horse the fewer tries it takes to get the right step.
OMG that was wordy. Sorry that you have to read all that, but I did my best to get my point across as clearly as I could.