Swipe with your finger over the flying ball to swing the bat. End the swipe when the ball reaches the strike zone to hit it. The length of the swipe will determine how far the ball will go and the direction of the swipe will determine in which direction it will fly.
Try to land the ball close to red flag on the field - each time this gets you a new baseball card to build your vintage card collection. The game contains 50 cards from the T206 baseball card set from the early 1900s, featuring superstars like Ty Cobb. Finding cards with better batting average will improve your chances of scoring home runs. If you are lucky you might even find the super-rare Honus Wagner card. More cards are coming in future updates of the game.
Use the experience generated by playing games to train your player stats. Upgrading the power and accuracy of your player will let you score home runs and find new cards more easily. Opening the game each day will also give you bonus experience.