Air Calédonie, with an office at the airport, has two or more flights a day from Nouméa. Inquire about flights from Lifou. Public transport doesn't exist on Maré, but the gîte owners pick up guests at the airport for a fee if they've been forewarned.
No car rentals are available at the airport, but the gîtes rent cars. If you take one, make sure the fuel tank is full; Maré has been known to run out of gasoline. Renting a bicycle at a gîte is another option and hitching is also possible.
The interisland ferry Betico calls at Tadine on its way to Lifou or Nouméa. Check the times before leaving Nouméa.