I imagine you are DPSing, so your life is usually the easiest in a M+ scenario, since you don’t really have to worry about following a specific route.
Start with the basics, read the journal and see the boss’ abilities then move to M0s so you can actually see things in practice.
Don’t just turn off your brain, pay attention to what trash mobs are doing and try to see what spells might be problematic with higher damage. Once you run each dungeon on a m0 to get used to the layount and the basics of each boss, move on to m2’s.
Keep in mind that your desire to learn is not shared by everyone in the group. You will notice that a lot of people will be utterly clueless and/or toxic while running lower keys. Don’t let that get to you, persistence is key and each failed dungeon is an opportunity to learn.
Run a few M2’s to get use to the idea of having a timer. Keep in mind that the timer for a low key is pretty much irrelevant. You either crush the dungeon and finish with a lot of spare time or have your group die 30+ times and brick the key.
Lower keys are not about speed, they are all about doing mechanics right and not dying a thousand times. Most mechanics are also very forgiving as failling something won’t be an instant death on the majority of cases.
People shouldn’t care much about your score while running keys around the 2-5 brackem but the best way to get invited to groups is by running your own keys. People should be far more concerned with your ilvl than your score.
Once you are feeling that your graps on both the dungeons and your class are good enough, move to a higher key. Things do begin to get considerably harder on keys 7+, but if you have a good grasp on the basics you should be fine to farm and learn from 7’s all the way to 10’s and beyond.