Argus became playable for all players in the 7.3 patch of WoW, but some players are reporting problems getting to Argus in the first place. Most players will automatically get the quest The Hand of the Fate quest when they log onto a character after the patch, but some do not.
If you are one of the players who do not automatically get the quest, what you need to do is to complete the Broken Shore Intro scenario. This can be done by talking with Archmage Khadgar in Dalaran (alternatively by opening the Adventure Guide and accept it from there), and does not take too long. After this has been completed, you will get the quest required to go to Argus, and you can begin your new Argus adventures!