All of this needs to happen within more/less 1-3 seconds:

Plan where you want your turn, energize heading into the turn, turn the outside shoulders through the turn to ensure straightness, energize again coming out of the turn by closing the calf, but then half halt with the seat and possibly the outside fingers, then close your calves again and ride forward into the connection, stretch up tall and engage your core, original lead inside leg at the girth, original lead outside leg may be slightly back to keep the canter lead until you ask for the switch, make sure you get the timing right, not too early, not too late, sit deep in the saddle, maybe a little pulse with the calves with the rhythm of the canter, then switch/swing the legs to reverse their position to ask for the new lead, open the hip and swing the hip to ask for the new lead, support with the leg to keep the jump in the change, ask for new bend and new flexion in the new lead by closing the fingers and possibly bringing the new inside hand ever so slightly closer to your body or ever so slightly away from the neck, collect/rebalance the stride with your seat and core to ensure they don't elongate due to the change, you might also need to close the fingers slightly, keep the calf supporting to ensure they maintain the correct amount of energy.

 

Now if you're doing tempis, prepare to do all of that all over again in the next stride or couple strides. 

 

Got all of that? Remember, do all of that within about 1 second. Maybe 2-3 seconds for some of the prep work.

 

This is why true, well-executed riding can be so challenging and takes a lot of time to truly master. You can become "proficient" in just a handful of years. But true expertise takes many many more years, and it's a journey with no final destination. All of the above needs to become so second-nature to you that it all happens without a whole lot of thought anymore. Because if you have to think all of that, it'll take way too long. You have to feel everything and make adjustments on the fly by just gut reaction rather than having to think it through. But switching from knowing enough to think things through to knowing enough to instantly feel and react takes a LOT of time and practice and diligence in being present in your rides.

 

*Disclaimer, each horse's flying change aids can be slightly different and each horse may react slightly differently in a flying change, which could change how you would need to ride the change differently from described above.