For 1v1, the only way to get better is to practise.
I don't know if you are Horde or Alliance but for Horde in front of Orgrimmar you can easily find a specific class as a practice buddy and start duelling to learn the opposing class. For Alliance I'd assume Stormwind or similar.
First of all though, you need to know your own spells, which ones CC, silence, increase your attack speed or output, etc. If you do not know the strength and weaknesses of your own class it doesn't matter how many AddOns you use you will never go beyond a basic level of PvP.
Anyway, other than that, you need to learn what other classes spells do and why they use them and to which effect.
You should always try to think along the lines of:
"How can I counter that skill or maybe best avoid being hit by it"
"What is this classes weakness after they popped they CDs and what are that classes CDs"
You also will learn then that some classes always cast one spell to enhance another that is when you might notice, "Oh, everytime he/she casts spell
x I propably should silence him/her as he/she will cast
y straight after which always takes half my HP.
A tool which I found very helpful in helping me to remember the skill names and helping me figuring out in which situations they are used most often and why or to which end is GladiatorlosSA.
AddOn shouts out the names of the skills your opponent is executing which helps when you are focusing. It also helps teaching you what visuals you see on your opponent when they execute the spells and more.
Don't use the AddOn though in BGs as it is rather annoying to listen to 10 people executing spells :)
Again, no matter what tools you use, practice and making notes on classes and what they most of the time use when and why is your best bet for improvement.
It took me a few weeks of Arena and duelling before I knew a few classes well enough to anticipate and read several situations but it doesn't mean you win all the time, it simply helps you put up a good fight at a minimum :)