First of all, don't go buy some crappy guide that claims to make you better and is just full of info that pisses you off because you already know it. If you didn't know it, you're pretty much a freaking idiot. These guides are just summaries of the classes, but to improve you're overall PvP and PvE performance, you have to do more then just learn about you're lore in the game. Its all "ORLY I C WUT U DID THAR" crap.
Start by doing this. Go on the AUTHENTIC World of Warcraft Forums, and look around the topics. Find out what the hot spec is and get it. This doesn't necessarily make you better, but it can if you truly LEARN the spec by testing it.
Now that you have the spells to your new spec, keybind them. Keybinding is a huge factor of PvP and PvE because its faster to react and hit spells other then clicking and keyboard turning. Try hiding your action bars to learn where your bindings are yourself. Products like Belkin SpeedPads are incredible and will be sure to improve you in PvE AND PvP departments. (I am not advertising for them, just merely saying they are very useful)
Macros. These are important if you want to reduce your keybindings, or merely just improve them. For example:
/stopcasting
/cast counterspell
This macro improves your spell because it works for both when and when you are not casting as a Mage. Get the idea? K. Good. There are a ton of useful macros at Wowiki.com, as well as the Official World of Warcraft Forum.
Train yourself by practicing with a buddy (dueling) or joining some PUG BGs.
Whenever you have a question look to the Official Forums, that is the #1 source by far.
If you still suck after practicing these techniques after a week or two, well, you just suck. Go buy the "ORLY" guides and start this over again.
Hope I helped. L2P now. :wave:
Feel free to add to this, just don't add crap that you learn from the trade channel.
Oh, and I'd make a PvP video, but I was hacked and on the road to level 70 agian. Just hoping when I ding 70 I'm not around idiots.