Con Son airport is located on the North of the island. To get into town, either book a hotel in advance which will provide you pickup service. Or hop on one of the hotel buses. They will drop you off in town for 3 dollars, from there it is an easy walk to just about anywhere. As of now, there is no taxi service in Con Dao island.
Car hire with driver is available from $70 per day. The main town is quite small and still has many charming houses and shop from the colonial period, all within walking distance.
However, you will get the most out of your time here if you can rent a motorcycle to explore the other parts of the islands. There is so little traffic that you can enjoy the experience of freedom zipping around and exploring.
Please be aware that there is only one gas station on the island with very limited hours. To avoid any hassle, you should rent a well maintained motorbikes with a full tank of gas.