One great way to get to/from St. Martin is by ferry. It's easy to get to Anguilla for instance:

There are taxis outside the airport terminal, just tell the taxi driver you want to go to Marigot ferry terminal (cost approx $20). Once there, go to one window and put your names and passport details on the form. Then go the the next window and pay for your departure tax ($3 each).

When you arrive at the ferry terminal, a guy will take your luggage and put it on the boat for you, make sure to tip him!

The boat leaves every 30 minutes, last boat at 6.30 pm, you can't reserve a space. Pay onboard, around $12 per person. On arrival at Blowing Point, another guy will take your luggage and deliver it to you after the immigration (passport) and customs check.

Tax - St. Martin now requires you to pay a tax upon departure. Make sure you have enough cash with you. Persons returning to the United States pay $30.

 

Most people will arrive on St Maarten at SXM/Princess Juliana Airport.  It is among the most modern and newest airports in the Caribbean and likely the second busiest to Puerto Rico's San Juan International.  Direct flights are available to/from various locations in the United States on Delta, Continental, JetBlue, Spirit, American Airlines, United and US Air; to Canada on Air Canada, WestJet, CanJet and Air Transat; to Europe on KLM (Netherlands), France on Air France, Air Caraibes and Corsair; and to/from various other islands in the Caribbean on American Eagle, Liat, Winair and several others. Air Berlin has dabbled with service from Dusseldorf during the 2010 season... it is uncertain whether the service will continue. There is also puddle-hopper service to the neighboring small islands of St Barts (MANY flights per day), Saba, Anguilla, St Eustatius. The French side of the island has its own airport on the North end, at Grand Case, but it only accommodates smaller propeller driven planes and is rarely used for international travel.  During "season" flights are generally available on all the above carriers daily or nearly daily.  During the off-season (March or April to November), flights may be discontinued entirely or - more commonly - weekend only service of Friday-Sunday or the like. When booking flights, the departure tax is included with most of the larger carriers (e.g., Delta or KLM) but likely not included (and must be paid prior to departure, at the airport and in cash) with smaller inter-island carriers.

Upon departure, note that there is no sit-down restaurant at the airport available  after passport control and security have been cleared - there are only 2-3 take out stores and their offerings are very basic.  There is a sit-down restaurant, but you access that from within the airport before clearing security.

Ferry service is available to most of the neighboring islands, though schedules vary widely from every hour or two during the day to Anguilla to one to two times per day or less to Saba.  Some ferries originate from Marigot (see above), but most start in Philipsburg or in Simpson Bay on the Dutch side. Though it is slightly smaller than the French side, tourists tend to frequent the Dutch side much more, as the bulk of the tourist infrastructure is located here - the main airport, cruise ship terminal, casinos, larger hotels, more Caribbean side (placid) beaches, more condominium options, etc. Aside from the Orient Beach area and mostly day or meal trips to Marigot and Grand Case, the majority of tourists will make their temporary island home on the Dutch side.