This is probably the most important rule besides "The Basics". Without this hefty level system things will be unorganized and not fair. So here's the deal, you have quite a couple ways to raise your Pokemon's level. I'll explain each way.
Battling Wild Pokemon
Throughout your adventure you will always be with and around wild Pokemon. Like the name suggests Wild Pokemon are wild and untamed which means you have two options. You can either battle then win to give your Pokemon experience or you can catch it. Here is how many wild Pokemon you'll need to battle in order to level up your Pokemon.
Pokemon between the levels of 1 and 20 need ONE battle to level up.
Pokemon between the levels of 21 and 50 need TWO battles to level up.
Pokemon between the levels of 51 and 80 need THREE battles to level up.
Pokemon between the levels of 81 and 99 need FOUR battles to level up.
Trainer Battle
This method of leveling up is quite similar to battling wild Pokemon, except you battle tamed Pokemon. No, you may not try and catch the other person's Pokemon, sigh, but you get experience! The same scale is used for trainer battles.
Pokemon between the levels of 1 and 20 need ONE battle to level up.
Pokemon between the levels of 21 and 50 need TWO battles to level up.
Pokemon between the levels of 51 and 80 need THREE battles to level up.
Pokemon between the levels of 81 and 99 need FOUR battles to level up.
You may also decided to wager an amount when you battle. Like say this for example. (Do not post like this >___>)
Ex.
Person1: Hey, do you want to battle? If you lose than you'll have to give me 700 Pokedollars but if you win I'll have you pay you 700 Pokedollars.
Person2: Sure, I accept.
Like in the example, the other person MUST accept the wager.
Training
There is also an option of plain out training your Pokemon. Training your Pokemon can be anything like swimming, jogging, hitting targets etc. You have to get approved by a mod or admin for your Pokemon to level up that way. Here is the number of words you'll need to level up your Pokemon.
Pokemon between the levels of 1 and 20 need a post of at least 200 words to level up.
Pokemon between the levels of 21 and 50 need a post of at least 400 words to level up.
Pokemon between the levels of 51 and 80 need a post of at least 600 words to level up.
Pokemon between the levels of 81 and 99 need a post of at least 800 words to level up.
So that's that the gist of it. Training your Pokemon in your free time is a great way to increase your Pokemon's level quickly.