How do you get to the lich king in icecrown citadel?

Step 1: Get to the Icecrown Citadel instance, which is located at the stairs West of the Wrathgate in Icecrown.

Step 2: You need to defeat all the bosses of each of the wings (Saurfang, Sindragosa, Professor Putricide, Blood Queen Lana'thel) to activate the teleporter.

Step 3: The teleporter in the middle of the instance (between the entrances of each wing, suspended from chains and with Val'kyr flying around it) leads to the Frozen Throne.

Note that in order to be able to attack the Lich King in hard mode, you need to also have defeated each of the wing's End bosses on hard mode.