Three things make scrambled eggs creamy: low heat, constant stirring, and stopping early. At low heat, the egg proteins set slowly; constant stirring keeps the curds small and the mixture creamy. Because the eggs continue cooking after the pan is removed from the heat, take them off while they are still slightly wet. Add the salt at the end of cooking as well.
The texture of scrambled eggs depends on one thing: the size of the protein curds that form. Small curds give a creamy result, while large curds leave a lumpy, dry texture. Two variables determine the size of the curds: the heat level and how often you stir. High heat sets the proteins all at once and creates large curds; low heat slows the same process. So the cook is entirely in control of getting two different textures from the same eggs. That is why the heat level, not the cooking time, is the decisive variable in the same recipe.
That makes heat the first rule. Heat the pan over low heat, not medium, and pour in the eggs; impatience and turning up the heat directly ruins the result. As the mixture warms, it starts to set around the edges. The second rule is stirring: keep the spatula moving across the bottom of the pan and break up the set parts right away. Every second they are left alone creates a larger curd in that spot. Do not overheat the pan in advance either; pour the eggs into a warm pan and let the heat rise gradually. For a nonstick pan, choose a spatula with a soft tip; a metal spatula scratches the surface.
The third rule is the one most often missed: stop early. The pan stays hot after it is removed from the burner, and the eggs keep cooking. One egg that looks just right when transferred to the plate will be overcooked a few seconds later. So take the mixture off the heat while it is still slightly wet; the residual heat will finish cooking it. If needed, move the pan to a cool surface. Do not preheat the plate either, because a hot plate continues the cooking for a while. For the same reason, take the eggs to the table as soon as they are plated.
When you add salt also affects the result. Salt added at the beginning of cooking draws water out of the eggs and causes liquid to pool in the pan; you will see liquid under the eggs on the plate. So add the salt at the very end, after turning off the heat. Add a piece of butter or a spoonful of cream at the same time to stop the cooking and make the texture even creamier. Whether to add milk is a matter of preference; milk softens the texture, but too much makes the mixture watery.
A few details make the process easier. Do not beat the eggs for a long time before pouring them into the pan; mixing until the whites and yolks combine is enough. Choose a nonstick or well-seasoned pan. Use a silicone spatula with a flat edge because a wire whisk misses the corners of the pan. Do not let the cooked eggs sit; serve them as soon as they are plated. Add black pepper after removing the pan from the heat too, because pepper heated in the pan leaves a bitter taste. Do not let leftover eggs sit; their texture will not return when reheated, and they will become rubbery.