Hi Lily !
You can know it when you're riding your horse, you can feel if he is more comfortable and flexible on one side !
They tend to be more flexible to their better way. Another good clue is what way(right way or left) they ride the best.
It depends on which side is lighter
When you're trotting try doing a sitting trot with your eyes closed and then a rising trot. The horse will put you on whatever posting diagonal they are most comfortable with.
Ask to canter, see what lead he/she picks up naturally
which ever side they feel more comfortable and confident on
Whichever side is his/her best or strongest side
If he/she have trouble with picking up her canter one way that not her best way. Then the other one is her/he best way
Usually, you feel it when your horse has a hand where he feels better. He is more flexible on one side, is more comfortable, ...
it depends on which side is lighter
If you put them in a round pen and send them out like you are gonna lunge them which even direction they wanna go first is there dominant side.