If you're thinking about dipping your toe into BGs with the new random finder, DO IT! And use this helpful, if extremely basic, guide to make your BG experience fun!
Step 1: Accept you're probably going to die. Make bestest friends with the Resurrection Angel, and move on.
Step 2: The first time you enter any BG you will likely have NO idea what's going on or what to do. This is okay. Following the crowd is not a bad strategy. It's not ideal, but it's not bad. Once you've seen all the BGs at least once, I would highly HIGHLY recommend finding a good guide for each and reading it. Heck, you can do that before you even set foot in any BGs, but that doesn't work well for me personally. It doesn't make a lot of sense till I see them.
Step 3: Put any idiot QQing on ignore. You know, the people who start before the game has even started and keep saying how Alliance/Horde sucks, how this group sucks, how this or that person is an idiot for a piece of green gear. Yeah, IGNORE. They never have something useful to say about what's happening in the battle, so save your sanity.
Step 4: Rogues are evil, as are kitty druids. EVIL! Just saying. Especially if you're a caster, a rogue can shut you down so thoroughly that you go from full health to dead before you get a cast off. If you're playing a rogue or kitty, go forth and have fun (but if you see a baby shammy named Eiunn, please leave her alone. She's developing a kitty druid phobia from being ganked so often by kitties. They were even graveyard-stalking her!)
Step 5: Kill the enemy or heal your allies or both. If you're not a horribly mobile class, I would suggest finding something to guard (like a tower in Eye or Stables in Arathi). You won't get as much honor this way, mind, but it's generally far less overwhelming.
Step 6: Avoid flag-running and vehicles the first time. It is really annoying when someone picks up a flag and has no idea what to do with it, and ditto with a vehicle. Ranged and healers might want to grab a ride on a vehicle though, because healing/pew-pewing is much easier from cover.
step 7: Losses happen, as do wins. The queue for a new random in my battlegroup is darn near instant right now, so go try again. And either way you get honor and with enough honor you can get nifty nifty mounts. Plus epic gems and pvp gear to make you harder to kill! And given the honor boost (Garetia got 5k for an Arathi this morning), it's a pretty quick grind.