First and foremost, it is always polite to hold the door for the person behind you. Period. As the image of doors getting slammed shut in one's face is not a pleasant one, taking an extra 5 seconds of your time will brighten someone else's day and you will have gone one step closer to fulfilling your good-deed quota of the day. Of course, if someone holds the door for you, don't forget to say Thank You!
Second, let them out before you go in. This rule can be applied to subway turnstiles as well. I know it seems like common sense; however, that rule is forgotten by many. A person has a much easier time exiting through an empty space, rather than maneuvering through a crowd. After the person is allowed through the door, the passer-by-er should hold the door for those entering.
Now, the age-old question of gender and door holding. Modern times dictate that chivalry is no longer an integral part of society. According to an article in the Chicago Tribune (written by Nara Schoenberg) modern etiquette has a twist with "Etiquette for Dummies" by Sue Fox. When someone crosses to the door, the first person to arrive is the one who will hold it open, regardless of gender. A person's age may be taken into consideration.
The same is true for a revolving door: the first person to enter is either the first one to reach the door or the stronger of the group, if the door is not in motion.
Regardless of gender, teaching your preschool child to say "thank you" every time a door is held for him/her will cause pleasantly surprised looks from the grownups around. Everyone will notice "Paul/Polly Polite". Not to mention that young children like to have responsibilities. By assigning them a job, such as "door holder," children learn the skills of dependability and reliability, which will only help them in their future endeavors.
And of course, encouraging them to complete any task, regardless of age, race and/or gender is a valuable lesson to teach children (and one that we hope will stay with them for the rest of their lives)