How do I get to Orgrimmar from Silvermoon City at level 11?

In Silvermoon City you need to go the Sunfury Spire, pictured in the map below (it is near at the top of the map, near the middle). The Inner Sanctum has a teleport which will take you to the Undercity.

Directly outside the Undercity are zeppelin towers, pictured below. The tower on the left in the picture will take you to Orgrimmar. There are Goblins at the front of each landing pad who will tell you which city this zeppelin is for, and where it is on its trip (intended to give you an idea of how long you'll be waiting). For example: The zeppelin for Orgrimmar has just left Orgrimmar.

For anybody who finds this as of June, 2019 there is now a portal to Orgrimmar located on your right as you enter Sunfury Spire.

This is very easy simply go to Silvermoon City and go to the Sunfury Spire, go into the room at the back and there will be a portal that will take you to the Undercity. Leave the Undercity through the main gate and you should see the two zeppelin towers board the zeppelin to Orgrimmar and your all good