As a systems dork, I specifically recommend learning the three steps of spellcasting and the 8 steps of combat, as well as when, exactly, you are allowed to reveal enchantments, and how that process works. It's easy to gloss over and just play conceptually, or by copying other players, but the actual rules are worth learning.
And I'd add one of my own, that may seem contradictory, but isn't:
Learn to anticipate variance – Sometimes, when you're losing, your only real option to win is to luck out. You can stabilize if you manage to kill that Vamp, but you've only got a 20% chance of rolling high enough? Go ahead and attack if all your other options suck worse, and you'd lose anyway. Even make plans on the contingent assumption that the Vamp dies. You're dead anyway if it doesn't so there's no reason to plan for that. Sometimes it's ok to chance it, just remember that hoping won't change the roll. It is bad luck to be superstitious.
Contrariwise, if you're winning, consider playing more conservatively. You'll have more resources available to you, so make a plan B in case your plan A fails. Just remember to be alert for the Hail Mary from your opponent. If you can see it coming you can prevent it, and turn your opponent's calculated risk into a foolish gamble.
Why isn't this contradictory to Shad0w's advice? Because he's right: over the long term you will be as unlucky as you are lucky, and you should plan accordingly. Learn some rules of thumb to guess at probabilities, and keep them in mind when trying to predict what will happen. If you've only got a 20% chance of victory, you might as well take it, but if you've got other options, for the love of the Arena, do those instead!