Nachtblau, there is no process.
Seriously.
There are three things you need to know about the differences:
1. When the queue pops, you get a loading screen and are transported to somewhere in the continent you queued from. You are invisible to any players or mobs there. Your opponent doesn't see your character or name, just a random NPC's figure. You are anonymous. If you like, you can consider yourself facing a Mystery Tamer who is malicious and ingenious.
2. Your first pet doesn't (necessarily) go first. This is really hard for people who do PvE to get used to. When your opponent materialises, you will size up his team, figure which pet you expect him to start with, and then choose which of your pets you want to start with. You must choose: your first pet will not march out automatically.
3. There is a timer. The yellow bar on the bottom ticks down. If you let the time run out, you will Pass. If the ime runs out when you do not have an active live pet, the game will put in your next pet for you. If you let the time run out, you will have less time next turn. You will find you have plenty of time once you get used to it, but it's common to feel pressured at the start. Don't Panic!
The best start I can recommend to anyone new is to go do 8 or 10 battles with the full expectation that you will lose. If you win, great! but what you're looking to do initially is just get used to how the mechanics work. It doesn't take long. There is no penalty for losing; you just don't chalk up a win. Your pets are fully restored after the battle.
OK, then there's the "Compose your team" part of the game. Here are three meta strats that we're all sick and tired of, but they keep being played because they work:
1. Clonedance. Put down a Cyclone and switch pets and follow it with a Rain Dance, which buffs the hit and crit chance of the cyclone. The classic Clonedance is Blighthawk + S/S Jademist Dancer, but any pets with Cyclone and Rain Dance (or nowadays, Lucky Dance) can do it. Throw a third pet in to handle whatever is left - this is a place where Emperor Crab can come in handy. Axebeak and Junglebeak with their own Noct Strike that they can buff with Rain Dance is a more offensive alternative. MPD is also certainly a viable third. Or you could pick a tanky pet like a Humanoid Idol, Sporeling Sprout, Wyrmy. I've been known to start with a Haunter and then leave it in the back line until the end.
2. Darkness. "I see only Darkness before me". sigh. There is far, far too much of this around. I got nine - count 'em - NINE Darkness teams in a row from the queue recently. It's far too easy to be so powerful. Most of this is down to the Bone Serpent, which really really needs to be nuked from orbit. Darkness birds are at least easy to knock down. Keep Darkness up, keep Bones falling, Nocturnal Strike at every opportunity.
3. Haunt and Stall. Drop a Haunt on a pet, and stall while it ticks down. S/S Wicked Soul is the fashionable Haunter at the moment because of its speed, but the Kid and the Valk both work just fine as well. Anything fast with a Dodge works for stalling - Teroclaw Hatchling is ideal because of its heal, but a fast rabbit works great as well. You could make a beautiful example team: Ghastly Kid, S/S Fiendish Imp, Teroclaw. Start with the Kid. Dodge the first round if you expect your opponent to switch you out with an Imp, or Deflect with an Idol; otherwise Haunt. Bring in your Imp. Get your Immolation up and do a little damage until you lose 400-500 health, then Nether Gate your opponent out to be Haunted in the backline, then bring in the Teroclaw to Dodge and Heal while the Haunt ticks down, and the Imp heals from the Humanoid racial ticks on the backline. Darkness might shut you down, but it's a neat out-of-the-box strat for a lot of teams.
Or you might be more comfortable playing pets that you're familiar with. That's fine, at least to start. Just be aware that PvP is more about being
tricky than PvE is. You will face more dodges, stuns, traps and weather effects in a day than you have seen in the whole of your PvE career.
Discodoggy's older entries and Guides on http://pvppetbattles.com/ are still excellent for reading, but videos have become the main language of PvP. I really do suggest watching at least a couple to prepare yourself. But after that, the only way to get into it is to play, see what other people are playing, figure out why they beat you, and learn to do it to them next time!
Most undead with Haunt are going to be everywhere, so I'd suggest investing in a few. Curse of doom is also decent, that said I do find that the enemy pet dies before it goes off. Mostly, undead pets are going to be your friends in PvP
and while Llennoca and Gomirath seem to be taking a break, they both have a back-catalogue of good videos. Discodoggy also has a website http://pvppetbattles.com/ with discussion.
', and not queing at all, as there's no worthwhile reward for me outside of the 5k achievement, and not using meta could easily add weeks to any attempt to reach that point.