Rune Factory 4 gives you the chance to look over a town, while also handling a farm on the side, and acquiring new monsters to your barn. These monsters provide some great resources for you to sell or to use in cooking recipes. Obtaining new monsters can take a bit of time, though.
The first step you need to do is construct a Monster Barn on your farm. You can do this by visiting the Order board to the right of Venti. Check it out, and it should be under the development menu. Double-check you have enough prince points available to create it, and you should be able to have access to it after that.
After you build the barn, you can go find monsters out in the wild you encounter. To tame them, you need to throw items at them by holding the item from your inventory and giving it to them. You do not want to provide monsters any items with adverse effects because they do nothing to assist in taming them.
Eventually, you should start to see hearts above their heads with a speech bubble. There’s a chance the heart symbol will develop a skull next to it, meaning you have failed to tame the monster. However, there’s also a chance of the heart growing larger and then bursting, signifying you tamed the creature. You will have a much harder time attempting to tame a monster that’s a higher level than you, so make sure to choose the monsters carefully.
You should regularly check on your monsters to see if you acquire any resources from them to update your farm or cook any recipes available to you.