Hold the 2 puppet rods with 1 hand. To do this, you will want to cross the 2 puppet rods and hold them with the palm of your hand facing your body. Make sure that your little fingers rest on the rods immediately below the cross point. You can curl your fingers around the 2 rods and use your thumb and forefinger to move the rods.
Hold one arm rod and let the other rod go limp, if you desire. Many puppet arm movements require the movement of only 1 puppet arm rod. Allowing one rod go limp makes it easier to manipulate the other rod.
Be sure to keep the puppet arms in a neutral position unless you need to move the puppet arms for a specific reason. When most people talk, their arms don't move about. Try to imitate this with your puppet. Keeping the arms in a neutral position will give your puppet a natural look, and the arm rods won't end up detracting from the puppet during the performance.