Start with both arms ready to cast, and then run through the casting movements with both arms at the same time. When both arms are making the same motion, each arm helps to correct the other, possibly helping you learn faster. On top of that, you can watch all or part of both arms, adding another element of self-correction.
I have found Stroke Matching practice to be effective, even when one hand is holding a fly rod. By shadowing the rod-filled hand with the empty hand, you can get the benefits of this practice technique even as you get used to casting a line. Stroke Matching also prepares you to a degree for the skills of hauling.
Taking it a step further, Stoke Matching can be used to work on Side-Arm and Cross-Body casts. Start with both hands in front of your body, touching your index finger tips together. Keeping your fingers touching, run through various Side-Arm and Cross-Body Cast positions.
In order to keep your fingers touching you must follow (match) one arm with the other. In essence, you’re training yourself to make Side-Arm and Cross-Body Casts with both arms at the same time. When you practice a Side-Arm Cast with one arm, you are automatically practicing a Cross-Body Cast with the other. Not only do you get two-for-one, but you also get practice following along with the line hand, as well as re-enforcing muscle memory in both arms; one arm helps the other.