This guide will be a guide to the Stonecore instance from the perspective of a tank (a Protection Paladin, if you're wondering). I will point out difficult trash pulls and dissect each boss fight primarily from the perspective of the tank but with tips and tricks you can relay to the less awesome members of your group as well.
Upon zoning in, you will be faced with a simple-looking trash pull. This pull contains Millhouse Manastorm, a few Stonecore Earthshapers, and various other Stonecore mobs. Crowd Control priority will be the Earthshapers, whilst kill priority will be Millhouse Manastorm. Manastorm will flee when he reaches 50% health, so burn him down and then take out other mobs in an orderly fashion. When you engage an Earthshaper, his "Force of Earth" ability is important to interrupt. If he gets it off, he will turn into an earth revenant and eat your group. The next pulls are much the same, with Millhouse always running at 50%.
Boss 1: Worm
The first boss you reach will appear to be Manastorm, but when you approach him, a giant worm will burst out of a cave to the left and punt the little gnome a good few hundred yards into oblivion. This worm, Corborus, has a few abilities that are important to know. Until he reaches 60%, his main thing will be shooting Crystal Barrages at a random person. If he shoots this at you, you must get out of it quickly as it does damage, and spawns a bunch of crystals. These crystals must be AoE'd down before they reach a group member, or they will explode for 50k damage. Each.
When Corborus reaches 60% health (roughly), he will submerge. When he does this, the adds that spawn need to be picked up and kept off your healer. Additionally, long lines of dust will form, indicating the spot where Corborus will jump out and 1-shot anyone in his way. After he does this for about a minute, he'll emerge again and phase 1 will repeat. He'll burrow again at 20% and then be back up for the kill.
Moving on, you'll want to avoid the 2-pull flayers in the cave and pull each of the giants back to Corborus' spawn. The reason for this is that there is an AoE pull of crabs that respawn instantly, so are best left unengaged. When facing a giant, you need to focus primarily on his crystal ability - he'll throw a crystal onto the ground and it will have to be killed before it gets to anyone, much like in the Corborus encounter. You'll have to take one 3-pull of flayers as well as 3 separate giants, but you can avoid the rest of the trash in the cave. When you get out the other side, you have to run a gauntlet with dark circles on the floor indicating where a spike will fall.
Boss 2: Dragon
This fight is simply a movement and line of sight fight. You'll engage him and point him away from the group, as he has a frontal cone breath. Additionally, instruct everyone to move out of dust clouds as they will turn into lava pools which you don't want to stand in. He will then fly up into the air and drop spikes onto the ground. These will be signified by their dark circles, much like in the pre-boss gauntlet. When this finishes, your healer's job will be to keep LoS to you and your DPS' job will be to keep LoS to your healer. The same mechanics from earlier will still happen, but he will also do a Crystal Gale. When he begins casting that, you need to LoS him by getting behind a pillar (it has to be outside of his hitbox too, learned this the hard way), otherwise you'll get killed. Rinse and repeat.
Pre-Stone Giant trash
You'll now enter an area with twilight cultists. Besides CCing as much as possible, make sure to kill Twilight Sentries ASAP, otherwise they will summon reinforcements. If you have a warlock or a shaman, remember that some of the mobs are elementals and thus susceptible to additional CC. Watch out for the Rift-Callers, as they will summon imps and need to be CC'd or focused down first.
Boss 3: Stone Giant
This is a fight that is almost entirely on the tank. You need to keep him tanked facing away from the group. He will periodically cast a frontal-cone AoE. You need to get out of it, it will kill almost anything within a 30 degree arc in front of him. Additionally, instruct every member in your group to do some damage to him when he puts up his Bulwark/Spike Shield. This damage will get reflected back to them, which would be bad were it not for his next ability, Paralyze. This will hold everyone in place, stunned, but it is broken by damage, like the damage reflected from Bulwark/Spike Shield. After he casts paralyze he will begin casting a Huge AoE that will kill anyone within 15 yards of him. You need to get out of there as soon as paralyze breaks. Tip: As a tank, you want to run away from him in the opposite direction as the rest of your group. This way, when he finishes his AoE, if he decides to do his frontal cone immediately, it won't hit your unsuspecting DPS.
Pre-Last Boss Trash
There is a gauntlet here with a bunch of AoEable mobs. Additionally there is a big ogre-thing. Try to not have to deal with them both at the same time, but honestly, if you've made it past the first and third bosses you can handle the whole room here at once.
The final boss is a pushover compared to Corborus or Ozruk. You simply need to not stand in the void zones she creates, as well as killing the adds she summons (you can drag 'em through the void zones to kill 'em for bonus points!). She'll also force grip the tank, which is interruptible but not a huge deal if let cast. Finally, she'll shield herself and go to her altar. She'll start chucking huge rocks at the group, you can see where they will land by the dust effect, don't be there at the same time as the rock. If you can handle that, she'll be dead in a few minutes and you'll have a Winter Veil hat if you do it within the next two weeks or an achievement and useful entry-level raiding gear if you do it within the next two years.