The rider's weight aids make or break the canter transition. To get the correct lead, you want to make the outside heavy. By weighting the outside, it makes it easy for the horse to step off with the correct lead on the inside front leg.
So, how does the rider set up his/her aids for success?
1. Change your post 5 strides before you plan to make the canter transition. This just sets up the weight aids and timing a bit better for green horses. Eventually you won't need to do this on a trained horse.
2. Look over your inside shoulder. Don't just look over it, look behind it. This puts the weight on your outside seatbone. Make sure you don't pinch with your inside leg when you do this.
3. On green horses, open your inside elbow (push your hand towards the bit to make a little loop in the rein) the moment you ask for the strike off (this gives them a little room to turn their head to the outside and step forward with the correct inside canter lead. When they become more trained you transition to lifting the inside rein to keep contact).
4. Bump or touch your horse with the inside leg at the girth and your outside leg just a bit behind.. You should not have to squeeze. It's just a touch, and your leg shouldn't move backwards - only closer to the horse.
If you are still having trouble picking up a specific canter lead, check your shoulder and rib cage. A lot of riders seem to collapse their left shoulder. If you look behind your left shoulder for a left canter lead and still end up with the right, try picking up your left shoulder to your ear for the transition. That usually fixes the issue.