@Valkan What-the- Of all the songs you could have gone with, you pick a Champion Battle Theme for your FIRST battle!? Isn't that just slightly blowing it out of proportion!? XD
Anyways. Nicely posted.
@TheIrishJJ Oh, alright. So, when two players square off (which has never happened yet) it happens one out of two ways. Either the GM supervises, in which case the players tell their battle-plans and counter-battle-plans in their posts and I then resolve what happens. Goes slower, but will be fair. Bo chance of autododging. This is how all players play agains wild Pokémon and NPC trainers.
Other option is that you do it on your own. Then the two of you simply play according to the basic rules of roleplaying battles, as Valkan gave example of. This gives you both considerable freedom as to what will happen, and it will go a lot faster. It does depend on you both being respectable roleplayers that act maturely and for the joy of roleplaying, but that's hardly a problem~!
You always pick from your move-pool för attacks, contact with enemy outside moves is Struggle and hurts both Pokémon. What each move does is directly taken from what they do in game, and they perform as represented by their in-game animations or as common sense would decree. Super-effective moves do double damage, and yeah. Mostly like the games.
Now, when moves actually have a random chance of having an effect, I actually tend to roll a die. I do that for unpredictable things like if a Confused Pokémon hurts itself, if an Ember burns or if a Wild Pokémon is captured. Of course, in GM-less PvP you can always decide such things yourselves. But as for hitting, I use common sense. It's harder to hit here than in the games, the enemy will actively dodge. Conditions might also impact, like if a Pokémon is rolling then touching might be dangerous, a Pokémon on higher ground with a projectile move may have an advantage...
All in all, use common sense. I wasn't entirely sure what version of "how to battle" I was to answer. Haha.