The majority of car batteries today are maintenance free and carry a performance indicator so there are generally no physical checks you can perform yourself, except to make sure that the terminal connections are tight and free of debris. Make sure the terminal connections are kept clean to avoid a build-up or dirt and grease. You may want to coat the terminal connectors with petroleum jelly to help prevent the build-up of corrosive material.
Remember to take extra care when tightening the terminal connections. Over tightening can result in damage to the battery casing or lead posts and ultimately, premature battery failure. Beware of crossing or connecting the positive and negative terminals as this can result in an electric shock, irreversible damage to the battery cells and, in extreme cases, an explosion.