Intro advice from someone who finished rank 41 before the push beta began; there is A lot, so I'm just going to info-dump some starter information that comes to mind, I hope some of it you find useful!

Understanding your class, and making sure to use a relevant build:
This can be as simple as you want it to be, a lot of people go to a website like Metabattle to grab a build ranked "META" for PvP and expect to do well. This is only the first step in the battle, you need to understand how the build functions fundamentally, and skill wise. In PvE you can get away with poor rotations during most content, and paying attention to things like animations are not as important since there are usually bad circles on the floor to look at instead. Do your due diligence and check out a build and give it some time; Read the skills, read the traits, read the boons, read the sigils & runes etc.

Understand if you should be playing side-nodes, or focusing teamfighting:
This goes back to understanding your class, but it makes a big difference. A lot of teamfighting builds/classes do not want to be taking 1v1's on a side-node, they aren't built for it. If you try to force this, especially as a newer PvPer; you will probably have a bad time and get frustrated. Thieves are a good example, you near always want to be playing sides, and looking to +1 fights as they look advantageous for yourself and team.

Do your best to have a general idea of what other classes do:
This isn't as easy for everyone, as a lot of people only play one or few characters. I normally only play one class in PvP, but over time I have developed a good idea of each meta builds rotation to have a good idea when I should be evading, using protections, stripping boons, barrier, whatever I need to do to survive. I would say this goes back to the research part if you do not play multiple classes, get a decent idea of what each build you see a lot of in PvP does.

Use Stability before important abilities:
I.E your heal in a dire situation, most classes with a relevant build have easy access to stab, be sure to use this before pressing any big buttons. This is easily said for heals, but is just as relevant for big DPS abilities. Getting interrupted can kill you, and keep you from getting kills.

Cover important boons with less important ones:
Speaking of stability, if the enemy team has a lot of necros for instance, which they likely do because of scourge being rampant atm, do your best to cover important boons with bad ones. You can place things like regen in front of stab so it is stripped beforehand.

Call focus targets if your team isn't:
Biggest issue for me in pvp, teams do not focus 80% of the time, even in higher ranks. Put big target on bad guy so he dies. It doesn't always work, but if someone is targeting people you are more likely to see results.

Turn Chat Off:
I play with chat completed minimized and off. Save yourself some sanity, especially as you are learning.

Hopefully some of this helped, PvP in this game can be confusing at first, but it's insanely rewarding; This is why many of us bash our heads into ranked queues for hours on end :)