From the US it's easiest to fly via Puerto Rico and a connecting flight either with Sea Born or LIAT.
From Europe it's easiest to fly via Paris/St.Martin and a connecting flight with either Winair, Air Antilles or LIAT. However, cheaper is it to fly via Paris/Guadeloupe and then either Air Antilles or next day Ferry or private Little plane
From the UK there are different possibilities, either via Antigua, St.Lucia or Barbados.