The best way to reach Chennai will depend on the amount of time that you have and your current budget. There are some who opt to rent a car when they reach Chennai airport, which is one of the busiest airports in India. A lot of people enjoy this method because the ride can be very scenic and appealing.
Some would rather get a prepaid taxi so they can control how much they are going to spend. You can take the bus or the train if you are trying to save some money but if you have a lot of things with you, these methods may not be the most ideal for your needs.