I'm working on getting my horse to square up right now too, so I've been reading a lot and asking everyone for advice. Here's how I've been doing things so far (from the ground):
1. Walk straight, eyes up, straight line.
2. Ask for a halt with your body language first, then either rein or voice aid if needed.
3. Turn 180 degrees and look where her back feet are. If they are square, then cheer!
4. If not square, then observe how far apart they are. If they are a whole stride (step) apart, then ask her to step forward. If they are a short distance apart, then ask her to back. "1 step forward, 1/2 step back" is what I've been told, and I've found it true that my horse takes shorter steps backwards than forwards.
5. Now that her back feet are square (or square-ish) check out the fronts.
6. Again, "1 step forward, or 1/2 step back." Most likely, it'll be 1/2 step back.
7. Now that she's all squared up (or close enough) give lots of praise!
-Don't drill on getting square for hours. Just do a little, then maybe work on those pivots or something else for a while.
-After you get the backs square, while working on the fronts, she might move her backs again. No worries. Either start over (walk straight forward a little, halt, etc) or just focus on those back feet again, make them square, then return to the fronts.
-Don't be a perfectionist! If she's never been trained to square up, then give praise for the slightest attempt. Just moving the foot you were asking to move, in the right direction, is a success! She'll get more precise over time.
-Square up all the time! Bringing her to the cross ties for grooming? Square up! Having her stand at the mounting block? Square up! Putting her in her stall for dinner? Square up! Whenever you ask her to stop, ask her to square so it becomes natural.
-Remember, less is more! Don't yank on your mare's bit for her to back a tiny step. Just lean towards her a bit, and stare at that foot that you want her to move. Maybe take a baby step with your foot like you want her to do with her foot. While learning this new task, she'll probably be paying very close attention to your body language!
For showmanship you'll also need to learn to back straight and trot in-hand in addition to standing square and pivoting. Remember to practice these too! You may think backing is easy, but it better be straight! Try to back your horse straight through obstacles (cones, barrels, well behaved dogs
) so that she'll still back straight in the excitement of a show!