How do I get a pet? Can it attack?

There are several different types of pets you can get in this game. There are mount pets, card summon pets/monsters, and there are the pets that float around your head. Mounts can only be obtained from the Item Mall at the present time. Card summons will require that you have the umbra guide which you can get from Lebant the odd boy. Once you have the guide you will need to collect the cards from Umbra/monsters by defeating them, they will not always give you a card, so keep trying. Once you have the card go to your umbra guide and click Magic Square, add a card and click "use". If you want a summon that can attack, and help you fight you will need 2 cards of that same umbra/monster. Use the drop down menu in the Magic Square window to select Battle Summon. For the pets that float around your head you can get many of them from the Seal Tower quests. You can find this tower in the middle of Spiritual Land, which is just outside of Meteor Pit, and Thunder Hill. Other pets can be obtained from the Item Mall, and other special pets are dropped by bosses.