It appears that some gamers on the Xbox 360 are having issues with starting Dragonborn DLC. This problem has happened before with Dawnguard.
Skyrim Dragonborn DLC: how to start it (Xbox 360)
It seems that some gamers cannot find the tunnel which takes them to the new DLC. You should head to a town where the people there like you and avoid the ones that don’t. Paying a visit to the majority of towns in the game will get you started with Dragonborn DLC. You will be able to tackle guys in masks and once defeated you can then see their orders. These will show you a note with directions to Windhelm.
Videos have been posted online that show gamers how to start the Skyrim DLC and shows you the two masked men with their papers. A second video shows gamers how to start up Dragonborn by heading straight to Windhelm, you travel to the docks and talk to a man there. He will allow you to travel to Solstheim for a fair price. If you watch the second part of the video you can see the first 13 minutes of playing Dragonborn DLC, with the walkthrough providing help on how to start.
The Skyrim Dragonborn DLC for Xbox 360 will set you back 1600 Microsoft points. It is also expected to hit the PS3 but not before next year. Good luck!