In arena, your win condition will often be board control. How you go about this is different for each class, but generally speaking, making favorable trades and drafting some removal cards helps a lot. There are plenty of incredible arena players you can learn from, Trump, Guardsman Bob, Hafu, Ratsmah, Kripp, ADWCTA/Merps, etc.
fg can probably be spent on coaching, not sure what else unless you have DF access.
maybe wagering on battles, a tourney, etc.
Also, generally speaking, Paladin/Mage/Rogue are much easier to have success with in arena than, say, Warrior. Drafting is the most important part of the arena, and while others already recommended HearthArena, I'd like to say it's not the be-all-end-all. Yes, it's an excellent tool, but I suggest you check multiple player's tier lists and make your own decisions when you get more experienced.
This post was edited by Falcon_A on Oct 28 2015 03:24am