You begin Pokémon Conquest in the Kingdom of Aurora, which is mainly inhabited by Normal-type Pokémon. After talking to a few unnamed characters, you are challenged by two Warriors from the neighboring Kingdom of Ignis. This fight serves as a tutorial.
As soon as you start your game, you are immediately challenged by two people from another nation. How swell. As you enter the battle, it's two against one in this battle. But before anyone could move, a girl sends out her Jigglypuff to the battlefield. Now it's two on two. This battle is meant to be a tutorial, so you won't lose in this battle no matter what. The girl will teach you how to move and attack. So do that and take down the enemy like a boss. After beating them, they retreat back to their nation. After that, the girl, who is Oichi by the way, teaches you about your kingdom and how you can use it to become stronger.
When you enter the nation, you see a new area open up, this is a farm, where you can go there and train your pokemon and gain new allies to battle with, but the game won't let you have new allies just this yet. So go ahead and beat the enemies in the farm. Once done, you can wait a month in game. Once all warriors have moved (or delegated of dooing something), the game can let you move on to the next month. Or you can press X if you feeling like moving on anyways.
After moving on to the next month, another new area opens up. Oichi wants us to train more, so go there and beat the enemies there. Piece of cake. Now wait another month. I say now it's time to go and conquer some nations don't you think. Once you're ready, head over to the Ignis page to take it under your control.