The island is small — you can drive from one end to the other in under an hour — and a rental car is by far the most practical way to explore both sides. Cars are available from the airport and from several local agencies; rates are competitive. Drive on the right throughout the island. Crossing from the Dutch to the French side requires no documentation — the border is unmarked except for a small monument.
Taxis are widely available but expensive for inter-island distances. Agree on a fare before getting in. Shared minibuses run along the main roads on both sides and are cheap but slow and infrequent.
The French side has slightly better roads and almost no traffic except during rush hour near Marigot. On the Dutch side, the road around the lagoon to Simpson Bay can be very slow during peak tourist season. Walking is practical in Philipsburg and in Grand Case, but not between destinations.