The monsters you find inside of the caves can be convinced to live on your farm instead. All you have to do is order a barn from Camus (100 Wood and 1000 G), equip the Pet Glove, and wander into a cave to choose your creature.
In order to take a beast you're going to have to let it beat on you while you continue to press the B button to use the glove. If the glove begins to work you'll see little hearts appear above the creature's head. Some monsters are easy to tame while others take quite a bit more effort. Once you've tamed the monster you can give it a customized name. After you select its name the beast will teleport back to your farm to live.
Your monsters will need to eat Fodder to remain happy. You can buy it from the village stores or grow it yourself. When you harvest Fodder with your Sickle, the amount received depeonds on the barns built on your farm.
Total Fodder = Number of Barns x harvested grass
Each barn can only hold 99 pieces of Fodder, even though you may have more than that to harvest. Extra Fodder does not stack up and will vanish if you try to go past 99.
Everything you'll need to know to collect and take care of the monsters you can befriend. The creatures won't leave your farm unless you request them to return to their home world.
Some creatures can be instructed to work the farmland while you go out and woo the local ladies. Talk about cheap labor!
Any of the beasts can accompany you into the caves to help you with fighting. Just use the beast you like the best and you'll do fine.
Browse through all 63 creatures you can capture in the game. You can't collect any of the boss monsters you find at the end of each cave.