Don't. That's what we tell you as a car rental company and as island residents. Even though St Maarten is known as the Caribbean's party island, driving a car under the influence of liquor is not something you would do as a respectful guest to our community. On the French side, there are now very strict controls and you will get a significant fine if driving under the influence.
A valid US or Canadian license will be just fine. You do not need to bring an International Driver's License. And contrary to other Caribbean destinations, you are not 'forced' by the local administration to purchase a local driver's license for the duration of your stay.
There is a general speed limit on the Dutch side of 50 kilometers per hour, or 32 mph. Even though there are no speed traps or radar controls, very rarely will you be tempted to significantly overstep this limit.
The French side allows 90 kilometers per hour or 57 mph on some roads.
On the right, same as the US or Canada.
Both sides of the island follow European driving regulations; for Dutch Sint Maarten, these rules have been modified. Compared to the US, less of traffic is regulated by signage, because general rules cover more. As an example: Cars coming from the right have the 'right of way'. The only exception is traffic signs indicating otherwise. If there are no traffic signs, as the driver you must assume that traffic from the right will not stop for you. Be very careful not to just assume that you are on a major road and that cars coming out of smaller alleys have to wait.
Drivers on both sides of the island are usually very courteous and will show a high level of tolerance to visitors who are unfamiliar with local roads and driving habits.