I just ran heroic Neltharion's Lair on my Enhancement Shaman. Our tank was a Vengeance Demon Hunter who seemed perhaps a little inexperienced. We wiped on Dargrul several times, largely due to some mechanics that he was either ignoring or just not dealing well with. Unfortunately, he and our healer were antagonizing each other, and so when we got a new healer and managed to down the boss, he declared in the party chat that it was clearly just the healer. I tried to explain in a polite and helpful way that there were some things he could work on, but he left before I could give him examples (some of which were advice he had ignored after previous attempts.)
Anyway, given that I play four different tank characters, I figured I'd put down a bit of advice.
1. Tanking is not as hard as it seems
First off, tanking can seem difficult, as it's a bit like DPS but with more responsibility, but in fact it's a pretty different set of skills. As long as you can maintain threat (and unless you severely undergear your DPS, you generally can) you don't really need to worry about damage numbers.
Your healer has your back. All you have to do is make sure that the enemies are in the right position and that you do what you can to reduce incoming damage or heal back your own depleted health.
Basically, remember that you're not competing to top meters. If you survive the fight and you don't get your party members killed, that's a victory.
As a tank, it's your job to try to make the healer bored.
2. Situational Awareness
Healers usually just ignore enemies as long as they're not pulsing some AoE that you can't stand inside of. DPS can focus down individual enemies. In general, a Tank can't afford to do this. Any enemy that is in combat with your party needs to get at least a bit of your attention. Thankfully, just about every tank class uses the same ability rotation for single-target and AoE. So just make sure that you get your AoE attacks on everything you're currently in combat with. Sometimes that means moving, because if a party member strays off the path or hesitates long enough to draw some patrol you avoided, you're going to need to pick it up.
Most tanks have abilities I call "snap threat," which are instant-cast abilities that hit multiple targets and that are almost always available. DKs' Blood Boil, Paladins' Blessed Hammer (a talent, but a recommended one,) DHs' Infernal Strike and Throw Glaive, and Druids' Thrash are all good examples. Monks and Warriors might have a little harder time, but while they're less often available, Warriors' Thunder Clap and Monks' Breath of Fire or Keg Smash are also great for picking up adds.
Because enemies pay attention to you as the tank (assuming you got number 2 above right) you're going to have the power and responsibility to care about positioning.
First, there's the obvious: if an enemy has a big cone-attack that hits everyone in front of it, make sure you're facing the boss away from the group. Likewise, if it has any sort of tail-swipe ability that hits players who are standing at a particular angle, make sure that you're not wildly swinging the boss around. Whenever you can, plant your feet.
However, sometimes you can't. And you'll have to recognize when those situations arise. Some bosses make it obvious - like creating some big pool underneath them that you need to move away from. Sometimes it's less obvious - they might create a pool under one of your melee party members, and while you might be sitting high and dry, you'll still want to move the boss to make sure that everyone has a safe place to stand during the fight.
When moving a boss, be aware of effects that can be exacerbated by your movement. If the boss knocks you back periodically, don't back yourself up to a ledge that you can fall off of. If the boss has a tail swipe or frontal cone attack, make sure that you're not turning it to face your party or spinning that tail right into your friends' faces.
Also sometimes the boss will do something that even you shouldn't be standing in. If there's a frontal cone that they'll do without turning, quickly sidestep out of it, but be sure to get back into your position once the area is safe again to minimize how much your party needs to move.
4. Active Mitigation
Regardless of the fight, you'll always want to use Active Mitigation early and often. This takes a few forms, from increased avoidance to straight-up damage reduction to powerful self healing. In most cases, the effect is good enough on its own to be worth using. On certain bosses, however, there will be abilities that will specifically have extra effects (often doing significantly more damage) they hit a tank that does not have its active mitigation up. For bosses like this, you'll want to pool resources (and cooldowns) to make sure that you have the ability ready for when the thing goes off. (Though you also don't want to cap cooldowns or resources, as you'll still benefit from AM abilities during other parts of the fight.)
I highly, highly recommend using an addon like Weak Auras or something similar to track whether you have these effects up. Weak Auras allows something called "Progress Textures" which will allow you to have an icon that can either fill up or empty out as the buff wears off.
Let's go through each tank's active mitigation abilities:
Warriors: Both AM abilities are self-buffs. Shield Block has a set duration and will increase your block chance to 100%, which effectively causes you to take 40% less direct physical damage during its duration (or more thanks to Critical Block.) You also have Ignore Pain, which is a damage-absorption shield. This can be powerful when dealing with magic damage (that would usually go right through your shield) but can also wear off prematurely if the entire shield is used up. I'd recommend using Shield Block on any boss ability that cares about Active Mitigation, as you'll be guaranteed that it lasts long enough to still be up when the ability goes off.
Paladins: Shield of the Righteous is your main AM ability, reducing damage taken by a significant amount (based on mastery.) This is simply a 4.5 second buff that reduces incoming damage. Its effect (both the damage it deals and the reduction in damage you take) are increased if you're standing in your Consecration, so you should try to keep that up at all times. Additionally, Paladins have Light of the Protector, which heals you for a percentage of your missing health (again affected by Mastery.) This becomes more powerful the lower on health you have, but even if you're not dipping below 30%, it can still help out your healer. This heal does not grant any real buff, so it won't do anything for boss abilities that care about active mitigation, so make sure to use Shield of the Righteous for cases like that. Note that Shield of the Righteous requires you to be in melee range, as it's technically an attack that grants the defensive buff, so if there's a big hit coming in, make sure you can hit them first.
Death Knights: This one's a bit weird. The only official active mitigation buff you get is Blood Shield. If you're searching your spell book for this, you should stop, because it's actually your mastery passive. Instead, you'll want to be using Death Strike, which heals you for a big portion of the damage you've taken over the last 5 seconds (or 10% of your max health if you haven't been taking more than that amount of damage.) Your mastery will then generate a damage absorption shield that is proportional to this heal, and it's that shield that counts for active mitigation boss abilities. You do have other defensive abilities you'll want to use, but unfortunately these don't count for that type of boss ability. The main one is Marrowrend, which is a melee strike that generates three charges of Bone Shield. Each time you get hit with a melee attack, one of the charges on your Bone Shield will be spent to reduce the damage of that attack. Thus, you want to try to maintain at least one charge of Bone Shield at all times (or 5 if you have the talent Ossuary.) However, if you are sitting pretty on many charges, you'll instead want to use Heart Strike, which generates more Runic-Power-per-Rune-spent (15 for 1 or more if there are other targets to hit instead of 20 for 2) and thus means more Death Strikes.
Monks: Primarily, active mitigation for Monks is handled by your Brews, particularly Ironskin Brew. You can maintain very high uptime on this brew, which doubles the amount of damage you stagger from 40% to 80%. While this doesn't actually reduce the damage you ultimately take on its own, it will significantly smooth out the damage that you get, making the healer's job a lot easier. However, if you start to get a lot of staggered damage, you'll want to use Purifying Brew, which reduces your staggered damage by 50%. Be sure to use Keg Smash and Tiger Palm to reduce the recharge time on all your brews, but also be aware that Ironskin and Purifying share a cooldown, so if you use Purifying a lot it will make it harder to keep Ironskin up at all times. Ironskin Brew will be the buff you maintain in the event of boss abilities that care about active mitigation. I recommend taking the talent Black Ox Brew, which is a cooldown that restores you to your maximum Ironskin/Purifying Brew charges of 3 and also gives you full Energy. Because Black Ox Brew is a brew, its cooldown will also be reduced by Keg Smash and Tiger Palm, meaning you can use it very frequently. Aside from your Brews, you should also use Expel Harm to absorb any nearby Gift of the Ox orbs for a rather sizable heal, but again, the only real "active mitigation" buff you get is Ironskin Brew (actually, Fortifying Brew, your long-term defensive cooldown, might also count, but you can't use that rotationally.)
Demon Hunters: Your primary AM ability is Demon Spikes, which, much like Ironskin Brew, Shield of the Righteous, and Shield Block, is simply a buff that lasts a set amount of time. You get two charges of this and it only costs 20 Pain, so you'll have access to it pretty frequently. It also lasts a long time. However, another big part of Vengeance Demon Hunter survival is the use of Soul Cleave. This not only does a lot of damage to targets in front of you (and thus is good for threat in both single-target and aoe situations) but also heals you for a significant amount. It also draws in any nearby Lesser Soul Fragments generated by Shear, potentially healing you for a lot more than just its base healing. Basically, any time you've already got Demon Spikes up or on cooldown, you want to spend your Pain on Soul Cleave. Do not wait to amass soul fragments - while those will increase its healing by a lot, you'll be better served by getting the base healing of the ability and building up for the next one. Again, Soul Cleave does not give you an active mitigation buff, but its healing is a significant piece of the Vengeance survival strategy. You can pool Pain (though try not to cap it) before using Soul Cleave as it will heal you for more based on how much Pain is spent, I believe from 20 to 60.
Druids: I'll confess that my Druid is still sitting in the Dreamgrove having done almost nothing after getting the Claws of Ursoc, so this one's going to be a bit more sketchy. The primary AM ability for Guardians is going to be Ironfur. Unlike other tanks, there's actually a benefit to overlapping multiple applications of this ability, as you'll get the benefit of each stack (with each stack lasting its own separate duration.) Ironfur increases your armor by 100% for a few seconds, which of course will reduce the physical damage you take by a lot. This is the buff you'll want up when a boss hits you with one of those special attacks. Druids also have Frenzied Regeneration, which heals you for an amount based on the rage spent, but again, while this is a buff (it's a heal-over-time effect) I don't think this counts as true Active Mitigation for abilities that care.
5. Situational Awareness Again
As a tank you'll mostly be worried about enemies. But you'll also want to keep an eye on your party. Before charging on to the next fight, make sure that your healer has enough mana. Some healers will be fine with 50% or less, but if you see them struggling, it's ok to slow down a bit. If you see that the party is basically always at full health, you can pull a little faster or even take on two trash packs at a time (though make sure that these trash packs don't interact in dangerous ways - like having multiple healers or enemies within them that can cast fear on your group.) If instead your party is constantly at 50% health or dying, slow things down and try to employ stuns or crowd control to ease the burden.
Also, make sure that your party hasn't accidentally pulled something. Especially in Legion, there's a lot of dungeon trash that you can and should skip when possible. But all it takes is for one person (or one pet) to stray a little too close to them, or for some errant AoE ability to pull an enemy that normally is neutral, and you'll have some extra stuff to fight. Don't get too far ahead of your group.
6. Keep a Cool Head
Some players are awful. You don't need to do a ready check before every trash mob, but it's ok to take a second or two to assess your next fight. If you have a player who is pulling for you, you have a couple options. You can simply roll with it and pick up aggro on the things they've pulled, or you can politely ask them to stop doing that. If they keep doing it, you can try to get them kicked out of the group. You can also drop out of the group yourself if the party isn't cooperating, though this is definitely a last resort.
Ultimately, regardless of whether you're tanking or doing anything else, try to cultivate patience. Mistakes happen, and sometimes people are really just learning the ropes. Offer advice, but be sure to keep it in a helpful tone. If someone's being an ass, there's not much you can do about that, but if someone just genuinely doesn't know something - like boss mechanics or the optimal rotation for their spec, keep your advice friendly.