Challenge modes can't be queued for like normal or heroic dungeons; you must travel to the instances and start them yourself (at least until you start getting golds and can teleport to them). Doing so will illuminate why so few people enjoyed having to do this in the age before the Dungeon Finder.
Right-click your character portrait, scroll down to instance difficulty, and click the Challenge Mode option. The instance portal will change to the hourglass graphic above. Enter and you'll find the path forward blocked by a yellow mist with a sundial in front and a list of the dungeon's requirements on your right. Clicking the sundial will give you the option to start the challenge. Once you accept, you'll get a countdown from 5, and then you're off to the races. Be sure to pre-pot!
Filed under: Analysis / Opinion