Learn M+ and the dungeons as DPS. At least at first.
Start off doing 0’s, time all the dungeons, then do +2’s, time every one…
Understand how IO ( your dungeon experience score ) works, you need a score for every dungeon.
Understand with Low iLvl ( 583 is on the low side at this point ) and no IO it’s harder to get accepted. It gets harder the higher the level of key you’re trying to get into. Don’t take it personally when you get declined, it’s not.
Understand not every run will go well, there’s a fail state and there’s people having a bad day or not prepared to deal with that. If something goes sideways, go to WoWHead and look at the guides and figure out what it was, then go run it again.
Don’t take bad runs personally. The low level keys are usually the worst when it comes players unable to handle failure, give or take criticism in a healthy way, and blame others for their own mistakes. Sometimes it will be your fault, sometimes it wont. No big deal.
A “My bad” if you know you made a mistake can go a long ways to keeping a key going smooth. Lets the group know it was mistake, you know it was mistake, and no ones going to be able to fly off the handle and blame them for it.
Learning mechanics, when to use your CD’s, and when to use your defensives is the goal early on. If you’re playing the warlock you don’t need to worry as much about dispels and interrupts, but other specs you’ll need to learn what all the must deal with mechanics are. And as you go up in difficulty that list get bigger.
Experience is king. Just got to run them and take your lumps. Not every run will be great but it does feel good when 5 strangers come together, click, and smash a dungeon.