To see all the monsters in Rune Factory 2, you will need to visit the dungeons both during the day and at night. Some monsters don't appear until after 6:00 pm.
You can tame monsters with the friendship glove. When using the glove to pet them, you will notice hearts beginning to appear above their heads, even as they continue to attack you. Once you have successfully tamed them, you will be prompted to give it a name and it will head straight to your monster barn.
Different monsters have different tasks they perform and advantages they provide. Some don't do anything, such as the pomme-pommes, the cute little round red creatures you find in Trieste Forest. Monsters such as the pomme-pommes are kept basically for pets. Orc archers and orc hunters will not do anything, either.
Some monsters will help you with your harvesting. Goblin pirates and captains will water your crops, hobgoblins will harvest crops, titans will smash rocks on your farm, gigantus will clear boulders and minotauros will clear wood. Bees produce honey, which you can collect with a basket; buffamoos produce milk and woolys provide wool.
The monsters are divided into 30 different families: The Orc family, the Goblins, the Ogres, the Trolls, the Minotaurs, the Wizards, the Fairies, the Demons, the Spirits, the Elementals, the Golems, the Mimics, the Dragons, the Bird family, the Bovine family, the Sheep family, the Wolves, the Panthers, the Tortoises, the Squirrels, the Fish family, the Bees, the Ants, the Spiders, the Scorpions, the Beetles, the Slimes, the Mushrooms, the Flowers, and the "Others".
To build a barn, you will need $5000 and 50 wood. You will need to talk to the mayor in order to build the barn. You can easily get wood as rewards by completing certain requests.
You need to make sure you take care of your monsters by having food available for them. You can buy fodder from Mana's General Pumpkin Store. If your monsters aren't fed, they will not do any chores or give you any milk, honey or wool.