Walk. Most of Old Havana is eminently walkable – the best way to experience it. Traffic city-wide tends to be light by most urban standards, as few Cubans own private cars.
Otherwise, most visitors use taxis to get around. These come in many forms, from state-operated taxis (whose fares are theoretically meter-based) to private taxis (including a number of vintage American cars from the 1950s -even some from the 1930s and 1940s!), three-wheeled “Coco” taxis, and bicycle cabs.
You can hail them on the street, or at stands at prominent tourist attractions.