In general, I think the dungeons are very forgiving in ESO and allow for a wide variety of playstyles. Are some ways more efficient then others? Of course. I think where groups get into trouble in this game is when the expectations of each group member are different as to how a group should act.
For instance, if your tank wants to control all the mobs and your DPS want to AOE zerg everything, then you're going to have issues. And of course, in PUG's especially, it's not exactly easy to impose your will on the group. Sometimes you just have to adapt and plug the holes in the group so you won't be there forever. But my general advice is this:
If you're the tank - As Pyrrhic mentioned, you don't have that many taunts or aggro tools at your disposal so it's doubtful you're going to be able to walk every single mob on a string. If you want to play it the conventional way then you're probably going to have to ask the DPS and healers to walk the mobs back to you and/or focus fire on your target. Or you can just let them tank whatever adds themselves, which is not the horrible disaster it can be in other games. You should probably tell the others that if they insist on AOE pulling or kiting adds/bosses then they shouldn't expect you to save their butts if they can't do it themselves.
If you're the healer(s) - Like the tank, it's not always feasible or fun to expect the healer to do all the healing in a group. If you're in a more traditional dungeon group, then you'll have to make sure they wait for your magicka to regen before engaging. You'll also inevitably draw aggro and want to make sure to run to the tank so he'll peel them off you. If you're in a less structured group, then you might want to point out that sometimes they'll have to heal/mitigate damage themselves. I've been with groups where the tank is either incapable or unable to tank the bosses so they naturally come running after the healer. In this game, it's not impossible to kite tank a boss or two. Also, while we can rez faster with the skill points, it's not always the best idea for the sole healer to stop healing for 5 seconds while he channels a rez spell lol.
If you're the DPS - You will probably have mobs beating on you. If they are beating the crap out of you, it might be a good idea to run them over to the tank. It's probably a good idea to have some health pots with you, especially if you're prone to stepping in large red circles on the ground and not moving thereafter. Like with the healer, you are fully capable of kiting a boss or two. In this game, if the tank or healer goes down, the DPS can actually finish the fight or at least rez them back up. I know, it's shocking to experienced MMO players to think that the DPS has more responsibilities than just pewpewpew. lol.
In general, please stay out of the AOE. There is nothing so important that you are doing where you should just keep standing in the poo. I know it can sneak up on you sometimes but AOE damage is the only thing that has ever wiped me in a fight. I've had tanks go down, healers go down, etc but as long as you don't take too much AOE damage, things are still ok. On the other hand, you could be the most professional dungeon group in the world, but if you stand in the AOE, then it's not going to matter.
Sorry for the long post lol.