A good way of cleaning off corrosion from battery terminals is to mix some baking soda with water and pour the baking soda and water mixture onto the battery terminals.
The baking soda and water will dissolve the corrosion on the battery terminals and then you can spray it down with some water.
After you do that then use a wire brush or a battery post and terminal cleaner and clean the battery posts and battery terminals really good.
After that's done apply some petroleum Jelly to the battery posts and the battery terminals and then tighten the terminals back up.
The petroleum Jelly will keep your battery terminals and battery posts from corroding which can cause your vehicle to be hard to start.