In certain areas of the game, you will be teamed up with another trainer who will follow you and battle with you inside the certain area. There are a number of areas that do this. However while in the grass, you will still get challenged by Pokémon. However these will come in 2s and you and your partner trainer will battle them. While there are 2 Wild Pokémon out, you are unable to throw any Pokéballs, but if you defeat one of them, you will be able to capture the other. But be warned as the trainer you are with may inadvertantly defeat the Pokemon you are trying to catch.
Below are the places where you have these Team Ups and the Double Wild Battles: