First of all, post in the Battle Organization thread. Get a challenger and a referee - one of you will post the battle thread, declare the rules and send out the first Pokémon. You should agree any rules with your opponent. Also state how many Pokémon the trainers may use - 1v1 is easiest for the refs and you, though depending on the referee, using more Pokémon may yield more reward money.
The first poster will post what move they want their Pokémon to use - the Pokémon can use ANY move in its moveset, though every move will detract from its PP. Now, unlike in the games, there won't be individual PP for each move. A Pokémon will start with 100 HP and 100 PP. They will post 3 moves for their Pokémon, and may use conditionals (if they use Protect, use Amnesia, but if not use Aerial Ace, etc). For the ease of the ref's viewing, after you've said it in a more informal way, write it out like this (this is an example containing the above conditional):
Aerial Ace/Amnesia - Calm - Brick Break
The opponent will post their move, and the referee will do the maths and post the results. These will be the layout of the results (some referees may add more):
Pokémon
HP
PP
Status effects
Once the referee has posted, the opponent will post first this time. The order swaps with each posted round.