Rental cars are available at Princess Juliana International Airport at a dedicated area outside of the airport. You'll find a wide collection of rental car companies such as Leisure Car Rental (http://www.leisurecarrent...), Safari Car Rentals (http://www.safaricarrenta...), Avis (http://www.avis.com), Budget (http://www.budget.com), Hertz (http://www.hertz.com), Unity Cars (http://www.unitycars.com), EasyTerra (http://www.easyterra.com/), and E-Z Rent-A-Car (http://www.e-zrentacar.com) available at the airport. The roads are narrow, sometimes quite bad on both sides of the island, and often very crowded between Philipsburg and Marigot. See also "Stay Safe" below.
Note: At least one car hire/rental operator Rhino Car Hire insists that its cars can only be used on the Dutch side. This seems nuts, but when questioned they confirmed it email January 2014. Since several operators include a standard phrase such as "All cross-border travel disallowed" it's worth getting a specific ruling from the operator before parting with any money. Two brokers took the same stance, without saying which operator was involved.
Motorcycles, quads and scooters are also available for rent, however it is advisable that you have some experience on these vehicles before venturing into St. Maarten's sometimes very hectic traffic.
Taxi cabs are usually vans, which are geared towards servicing the cruise ship traffic. To go completely around the island will cost about USD25 per person. Most drivers are quite willing and able to hire-out as tour guides. Most charge USD45-50 per hour, and can offer a custom experience for 3-4 people that can be less expensive and more versatile and satisfying than large bus tours offered by cruise ships or hotels.
Saint Martin has a bus system using small minivans. You can recognize the vans because in the front window they will have a sign stating their direction and their license plate says bus. You can get most anywhere on the island for USD2 and the airport for USD3 most locals pay for their bus fare using USD. They run frequently between Philipsburg and Marigot. There are stops that the buses will stop at when someone is there, but you can flag one down from just about anywhere they can pull over as well as ask them to stop anywhere they reasonably can. They aren't exactly efficient or timely -- they show up essentially whenever -- but are a great way to get a leisurely tour for next to nothing and to get from the Dutch side to the French side.
If you are driving especially on the French side expect a lot of scooters and motorcycles to speed around you on both sides of the road. This can be startling to drivers not used to two wheeled traffic as it can create a dangerous situation. If you stay in your lane and don't waver you can trust most of the time that the cyclists will pass you safely. It's better to just let them pass you at a steady pace then try and slow down or pull to the side. Right-of-way is more of a suggestion; people will generally use their horns to let you know they're in proximity to you. It can be jarring, but as long as you don't make any knee-jerk moves, you should be fine.
Once you reach Philipsburg, Marigot or Grand Case, you can get around nicely on foot. The distances in each are not long. Take some care in Philipsburg and Marigot with heavy traffic, narrow, sometimes missing pavements, and the midday sun.