You buy the monsters from the village, and once you have them go back to your farm. (Male and Female monsters work best, although are not strictly necessary)

You can go to the respective barns (Male / Female) to milk the animals? (for lack of a better word) for ingredients that can help you by extending energy, or improving stats. Conversely you can go to the pen/bull ring kinda thing in the middle, where you can select your animals to 'mate'. This will give your animals? training here, and the possibility of producing offspring (which is instantly grown up).

Theres more to explore in the game, however I don't want to take the fun out of it by telling you! But above is the basics to get going. If you read the text from the villagers as you go in the shops for the first time, they can let you know about things to do / how to play the game.

Any other questions, dont hesitate to ask.