Resilience vs. damage
I've written about resilience until I'm blue in the face. We all understand why it's important: It reduces incoming damage from other players. At this point, you can reduce said incoming damage by well over 40%. Much higher numbers are possible, but let's play with 40% for a second.
Let's say you're fairly well geared for PvE, can produce your damage rotation reliably, and know what you're doing. You have a DPS of somewhere around 30k. (I know, I know, you're awesome and do more. I like 30k because it's a round number.) Against me, in my standard 40% resilience gear, you're now merely doing 18k DPS.
At this point, I tend to hear people shout about the fact that PvP gear puts out less damage, since it swaps out damage stats in favor of resilience. That's not false. The argument would be relevant if the combatants are two mages lining up 40 paces from one another, throwing spells back and forth until one of them falls down.
The reality is that PvP combat doesn't work like that. You rarely get through your entire priority list. Usually, you get one or two attacks off and then you spend an hour and a half running around in circles struggling to get another shot at attacking. (Some rogues in Battlegrounds look like they're having seizures, flailing around the map like floppy, overexcited puppies.) Since you don't get your entire rotation off, those damage stats all interact differently with one another.
It's pretty rare that you'll be in one-on-one combat, anyway. Even in the Arena, you have a partner. Dead characters do no damage, so if you don't have resilience, you're essentially a speed bump. Your little bit of extra damage from PvE gear won't help you when you're dead.
Get honor, buy gear
The best PvP gear is available from conquest points. Sadly, just like PvE valor points, you're limited to how many conquest points you get each week. If you wait for conquest points to buy all of your gear, you're in for a long, hard life. We'll all be playing pandas by the time you get done.
Grind honor, buy gear. How do you grind honor? Your options include Tol Barad, world PvP, and Battlegrounds. Here's the quick and dirty evaluation for each of the three methods.
World PvP isn't quite a myth. It does happen. It could happen to you. But it doesn't happen often or reliably, and never in sufficient amounts that you'll earn enough honor to buy all your stuff.
Tol Barad can be fun if you can grab a winning team. More often, though, it feels like a zerg of lemmings running face-first into a zerg of dodos. Only raw chance and random circumstances determine whether the lemmings or dodos will win. You should still do Tol Barad, because the reputation vendor has some good starting PvP gear. But don't hang your hopes on it.
That leaves the Battlegrounds. This is where you get your honor. It's also the point of most casual PvP, after all. You get the most honor by randomly stepping into a Battleground and then winning. Even if you lose, you'll get a nice chunk of honor pretty quickly.
Just keep doing that and buy all the gear you can. What order you go in doesn't really matter.
Follow some key advice
The rest of transitioning from PvE to PvP is following some time-honored, painfully learned PvP tactics that don't have good parallels in the raiding game. Most of these can be presented in bullet style.
Kill the healers first. They're balanced to require more than one person to kill. While you have a buddy alive, drop that healer immediately. The close cousin to this rule is to protect your own healers.
Don't fight on the road. No Battleground is won by fighting on the road. Fight near objectives. Fight the urge to get off your mount.
Yes, that class is that annoying. Getting tired of frost mages, rogues, and death knights? Don't worry, so is everyone else. But those guys have counter-classes they hate, too, so don't get frustrated. (OK, I don't know what counters frost mages, but I'm sure something does.)
Stay with the zerg. Running off alone doesn't make you a superhero. It makes you free honor. Stick with your team as best you can.
Switch up your strategy. If you detect your battlegroup has certain habits, do something radically different. Playing 20 Arathi Basin games this week, I noticed the Alliance go to the Mine, Stables, and Blacksmith every time. When a priest and I opted to go pay the Farm a visit, the Horde sure were embarassed (and they lost).
Stay away from the cliff. Accept the fact that a half-million boomkin and elemental shaman are eagerly waiting for you to get to the edge of a cliff. They're there. Even if the opposing side seems to have no druids or shaman, they will magically teleport into the match just to blow you off.
We'll do a Battleground summary for folks who are just getting started, so that you know more specifics for each game. That's where the real strategy and positioning comes in. It's also where our hope for humanity goes to die. For now, though, if you get started with these tips and go busily collect honor, you'll find your PvP experience infinitely easier very soon.
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to learning how to tank, getting up to speed for heroics and even how to win Tol Barad.