A dungeon master has many jobs, but they can be split into two categories; creating the game and running the game. With D&D 4th Edition, the basic rules can be quickly learned and more advanced rules will be encountered and incorporated naturally and gradually. After a few sessions, running a game should become almost second nature to a DM. Creating a game, however, can be a far more daunting task.
Anyone can imagine a fictional world, fill it with traps and populate it with monsters, but the art is in making it interesting to your players. The Dungeon Master's Guides are full of advice to help you create adventures that your players should find compelling; if you still don't know where to begin or don't have enough time, pre-made adventures and campaigns are another option.
My group have been playing a series of adventures released by Wizards of the Coast. The full campaign is a set of nine books that should take your characters from level 1, all the way to level 30. Wizards of the Coast released the first adventure as a PDF file that you can download for free from their site: H1: Keep on the Shadowfell
Keep on the Shadowfell is an excellent introduction to D&D 4th Edition. The adventure has an interesting storyline with plenty of background information for the DM to utilize as they see fit. The format of the book makes things as easy as possible for a first time DM. Each encounter has it's own chapter with descriptions to read aloud to your players and a map showing you how to place the enemies and traps. Every enemy has it's own stat block printed alongside the encounter, so you don't even need to cross-reference the Monster Manual. The book also explains rules that a new DM may not be familiar with, as they are encountered.
The series of adventures are divided into groups of three for each tier of play. The set of books for the heroic tier include Keep on the Shadowfell for characters level 1-3, Thunderspire Labyrinth for characters level 4-6 and Pyramid of Shadows for characters 7-10.
The set of books for the paragon tier include King of the Trollhaunt Warrens for characters level 11-14, Demon Queen's Enclave for characters level 14-17 and Assault on Nightwyrm Fortress for characters level 17-21.
The set of books for the epic tier include Death's Reach for characters level 21-24, Kingdom of the Ghouls for characters level 24-27 and Prince of Undeath for characters level 27-30.