Statia has no buses, so renting a car is useful if you want to explore the island properly. If you're staying in Oranjestad, you probably won't need a car for most of your stay but expect to do some serious walking as the town is spread out.
You can rent a car at the airport or in town. Your home driver's license is valid for driving on Statia. By Caribbean standards Statia's roads are good, albeit sometimes narrow, and you need to watch out for stray animals on the road. Drive on the right-hand side of the road.
There are usually one or two taxis on hand to meet flights at the airport, which is about a kilometer northeast of town.