Being a Dungeon Master is basically being a storyteller. You create the plot, paint the scenes, describe the action, and reveal the secrets.
There's also an element of being a referee, as you adjudicate rules and partially determine the success of actions.
There's also an element to improv. The group is creating a story themselves. The players are the protagonists of the story, each making their own tale.
The Basic Rules of the game can be purchased in book form. There is also a downloadable rules document online that contains the full rules of play and basic player options:
http://dnd.wizards.com/articles/features/basicrules
If you have not already purchased anything, I recommend the D&D Starter Set:
http://dnd.wizards.com/products/tabletop-games/rpg-products/rpg_starterset
It also contains the basic rules of play as well as an adventure, a set of dice, and pregens rated characters. You can start with that and get a feel for the game. You can buy that, skim the rules document, and be playing within the hour.
The included adventure covers hours of play, and from there you can move to another published adventure or create your own.
If you're just getting into the game and have no clue what to do or how D&D even works there are a number of videos of play. One example is the semi-official series Force Grey: Giant Hunter
http://dnd.wizards.com/articles/features/force-grey-giant-hunters
(It's a little on the mature side. I don't know how old your son is, so be warned. D&D can be as kid friendly or grown up as you want. You can run a game that is wholesome and rated G, or one that makes Game of Thrones look like children's programming. Up to you.)
Compared to other games, D&D can be complex. There's a lot of rules. But don't worry about trying to learn them all at once. You don't need to.
Get the basics down and just play.
Don't slow things down to look up rules during the game, just make a call and look up the actual rule afterwards. Keep things moving.