Good news is warrior tanks are very sturdy and pretty straight forward to play. You have the most passive armor of any tank, so even if you have a few seconds without Shield Block active, it’s very unlikely you will die. Delves are actually a good place to practice your rotation, and learning how to keep yourself alive and take as little damage as possible.
I would say the most important thing, outside of managing your basic rotation, is the route you pick and what mobs you pull together. There is a very handy addon called Mythic Dungeon Tools, which gives you an interactive map of all the dungeons, where you can see where all the mobs are placed. You can also inspect them to see their abilities, like spells to look out for. You can also import routes directly from other players.
I’m not saying you have to use this addon, but it helps if you want to do a bit of research before going into a dungeon. You don’t need to memorize a perfect route either. In the start, just focus on having roughly the percentage you need when you get to a specific boss.
With that being said, Blizzard has streamlined most of the dungeons over the years, so most of the time you can simply run to the next boss and kill whatever is in the way, and that will usually give you the correct trash mob % at the end.
Another reason the route is important, is knowing which group of mobs can be pulled together. Once you get the hang of your rotation, you’ll quickly discover that in most cases it’s not your survivability that limits what you can pull, but rather what the dpsers and healer can manage.
If there are too many casters in the same pack, people start dropping. If you pull 2 mobs which both have big, unavoidable AoE damage, the healer might not be able to keep the whole group up. It’s not uncommon for you to be sitting at full HP, while the group is struggling to live. A good example is the Shard of Halkias mini-bosses in Halls of Atonement. Don’t pull 3-4 packs on top of them. You might be able to live, but if some casts go off at the same time as Thrash is hitting the whole group, people are going to die.
I’m pretty sure if we have some healers in here, they can confirm that a huge frustration with inexperienced tanks is that they run in and pull 5-6 packs of mobs, like they are competing in the MDI, and group just starts dropping one by one. Then the tank proceeds to blame the healer. Don’t be that tank…
Most dungeon timers are pretty generous, and you don’t really need to do insane pulls to make it. You set the pace. Start slowly. Learn to chain pull, where you go into the next pack when the first one is low on hp, or you have killed the most dangerous mobs in it. This is generally much better than just yoloing into 5 packs with all your CDs, hoping the group can manage.