Double reins are used with a Pelham bit or double bridle, and they require more concentration and skill than normal snaffle reins because there is more leverage on the horse's mouth. Therefore, it is very important to hold them correctly and to use them with care. There are different ways to hold double reins, but some methods are easier than others and are better to use while you're learning to use reins.
Pick up the Pelham rein (not the snaffle rein) as you normally would. Lay your fingers on the reins as if you are picking up a teacup, and lace the reins between your pinky and fourth finger and your thumb and index finger. Make sure your three middle fingers are on top, your pinky is underneath and your thumb is on top. Point your thumb toward the horse's ears, and the extra loop of the reins should follow from the path of your thumb.
Hold the Pelham reins, and at the same time pick up the snaffle rein. Hold the snaffle rein in the same manner as the Pelham rein, and layer the snaffle rein on top of the Pelham rein. While holding the snaffle rein like the Pelham, put the snaffle rein under your pinky and your thumb (lined up with the Pelham rein).
Experiment with wiggling your pinky to use the snaffle rein, and using your whole hand (gently) to use the Pelham rein. Keep the reins even as you continue to ride.
You can also move the reins up so that the snaffle rein is between your pinky and fourth finger and the Pelham is between your fourth finger and middle finger. Talk to your trainer and decide which is more comfortable for you to use.
Remember that the Pelham is harsher than a snaffle bit, so you must be gentle and aware of how you are pulling on your horse's mouth.