Double doors, like double windows, can help a great deal to save heat, but first, two considerations:
-- The tighter of the two doors (better weather-stripping, better door) must be on the inside when the doors are on the same frame as moisture must escape outward.
-- Glass storm doors must not be put outside of thermal doors on the west, south or east sides of the house if the sun shines on the door: the temperature between the doors can get hot enough to melt plastic!
Storm doors are attached to the same door frame as the primary door. They can serve as screen doors in the summer. They do not save energy if the door is subject to strong prevailing wind, or if there is a lot of traffic in and out of the house. They are both open together at the same time.
Air-lock doors are second doors installed on the inside of the house, far enough down the hallway to allow closing of the exterior door before opening the inner door. The most thermally effective air-lock chamber is an unheated entrance added on to the outside of the house with a good thermal door on the inside and good weather-stripping on both doors. This creates the smallest quantity of heated wall space. This air-lock is really just a good wind break. Air locks are cost effective where you have strong prevailing winds blowing on a door or lots of traffic.