Simca has a cleaner write-up here if you want a better overview.

Patch 5.2 - The Thunder King

Time to chat up Wrathion again. It turns out the Black Prince has a very important guest in the tavern - Prince Anduin Llane Wrynn! He and Wrathion will talk about current events while you listen. (Meet Me Upstairs)

 After an interesting discussion involving Wrathion's and Anduin's chess game as a metaphor, Wrathion mentions that the Thunder King left some of his enormous power behind on the Isle of Thunder. Time to collect it for Wrat-- I mean, for us! Secrets of the First Empire requires 40  Trillium Bars and 20  Secrets of the Empire. The trillium bars are easy because this is an item that can be crafted by the Mining profession (and the mats quite literally farmed from your Sunsong Ranch if you so choose). The Secrets can be farmed only from 5.2 raid bosses in all raid difficulties; bonus rolls cannot award the quest item. The Secrets - or sekrits as my guild liked to call them - were much less painful for me to accumulate than the sigils for an earlier legendary quest, The Strength of One's Foes. Rate of acquisition is still a matter of RNG, so prepare yourself for another long slog anyway.

Alongside "Secrets of the First Empire," you will need to reach Exalted with The Black Prince. I Need a Champion's quest text suggests killing mogu, Zandalari, and saurok on the Isle of Thunder. (See my comment on  Speed Metal for my farming method on IoT.) However, any mogu on Pandaria and Alliance/Horde NPCs (depending on your faction) at the shore of Krasarang Wilds will award reputation. If there is a means of applying a bonus modifier to reputation gains, such as through the Darkmoon Faire and a few other world events, I highly recommend taking advantage of it.

The Thunder Forge requires that your realm unlock unlock Stage 4 of the Isle of Thunder. This should not be an issue because every realm at this point ought to have accomplished it. The more tedious part is that your character must be in the correct phase to meet Wrathion. You must complete the solo scenarios up through  To The Skies! [started by To the Skies! (H) / To the Skies! (A)].

Now comes the hardest part of "The Thunder Forge" - Wrathion's task. The solo scenario at Stage 5 requires you to know how to eek out every point of damage and very tightly time your survival CDs. I can guarantee a majority of players will die multiple times in the process. 

Next, you must take the lance you just acquired and use it against Nalak for Spirit of the Storm Lord. (The Fall of Shan Bu (H) / The Fall of Shan Bu (A) required to continue.) It doesn't matter which faction has tagged Nalak, nor does it matter what HP Nalak is at. While someone is tanking Nalak, you will need to kite the Essence of Storms. Do not attack and kill it or you will not receive quest credit - just kite it and it will slowly die as its energy is siphoned. Tip: You can ask a class like Paladin or Mage to get aggro on Nalak and then use their Immune-type ability.

Finally, an easy part. Return to the Tavern in the Mists and give Wrathion the  Tempered Lightning Lance. He'll ask you to meet at Mason's Folly. There, he talks about stuff I might actually be bothered to write here at some point. Anyway, listen to him and then choose your legendary meta gem! IMPORTANT: Make certain to closely read the tooltips of the meta-gems. If you didn't and you chose one not appropriate for your desired spec, you are able to purchase a different one from Blacktalon Quartermaster inside the tavern 5x  Primal Diamond.

Ever-insatiable desire for more knowledge about the mogu and the Titan technology they used, Wrathion's next mission for you is retrieving 12x  Titan Runestone from bosses within Halls of Flesh-Shaping and Pinnacle of Storms. The runestones can drop in any raid difficulty but only has a chance to drop once from each eligible boss per week. Lei-Shen now has a 100% drop rate (source) so the longest this quest should take is 12 weeks. Each time you loot a runestone, an image of Wrathion will appear and whisper you the information he has learned. (Apparently, if you aren't alive in LFR when you receive the quest item, Wrathion does not appear.) The dialogue in the whispers are voice-acted.

Yay, you've collected every runestone! Have a cookie. Wrathion wants you to return to the Pinnacle of Storms and slay Lei-Shen for his heart. What a delightfully easy task. Of course, if I'd known Wrathion would eat it...

Anyway, enjoy your  Chapter III: Two Princes achievement! Onward to earning  Chapter IV: Celestial Blessings from Patch 5.3 legendary content. (Starts with http://www.wowdb.com/quests/32598-a-reckoning.)