There will be spoilers for every patch of Mists of Pandaria, including 5.4 and the Siege of Orgrimmar raid, in this post
Leaving aside blame for a moment, let's just look at the results of the past year or so in terms of what actually happened. To heavily summarize events:
Horde and Alliance forces discovered Pandaria, landing in the Jade Forest.
Both factions mobilized local allies (the Horde made pacts with the Hozen, the Alliance joined forces with the Pearlfin Jinyu) and waged a proxy battle through these cat's paws. The result was the desrtuction of the Jade Serpent's next incarnation and the release of the Sha of Doubt, leading to the Sha infestation of the Temple of the Jade Serpent.
Both factions pushed onward into Kun-Lai Summit, where they fought the yaungol and set up base camps, converting local pandaren to their cause. They did not actually join in battle at this time.
Scouts and agents of the Horde and Alliance penetrated deeper into the continent, in time exploring the Townlong Steppes and Dread Wastes. In time these advance forces even managed to convince the August Celestials to allow both the Horde and Alliance to set up bases within the sacred Vale of Eternal Blossoms.
Both the Horde and Alliance made large-scale military bases in the Krasarang Wilds and began using these to wage resource war against one another, fighting over territory and raw materials as well as ancient mogu artifacts buried below the surface of the wilds.
This period of hostilities led to a culmination wherein Warchief Garrosh Hellscream attempted to use a mogu artifact, the Divine Bell, to infuse his own soldiers with the power of the Sha. The fallout from this action caused the neutral Kirin Tor to eject the Sunreaver pro-Horde faction from Dalaran and declare themselves for the Alliance under their leader, Lady Jaina Proudmoore. Prince Anduin Wrynn nearly died in the attempt to destroy the Divine Bell, which succeeded. Garrosh Hellscream, however, was not balked from his goal of finding a new weapon.
There's more, of course. Things had only begun to heat up at this point.