Things You'll Need
Instructions
Purchase battle pet training. Trainers selling this skill can be found in the starting zone for each race, as well as in Stormwind and Orgrimmar; once you've purchased this skill, all characters on your account will be able to participate in pet battles.
Press "Shift-P" and click "Pet Journal." Type "Great Horned Owl" in the Search box to find your owl.
Drag the great horned owl to the empty slot in the Battle Pet Slots list.
Click the "Tracking" icon on your mini-map and select "Track Pets." Walk around until you see a green paw icon on your mini-map -- this icon identifies the location of a wild pet that you can fight.
Approach the wild pet. When you are close enough, the paw cursor you get when you hover your mouse over it turns from gray to green.
Right-click the wild pet to start a pet battle. Press "1" to make your owl attack the enemy wild pet with its Peck ability. Continue doing this until the enemy pet is defeated.