Dominica is has only two airports but only one of them (Melville Hall) is used for commercial airlines. Melville Hall airport is located in the north-eastern side of the island so it takes about 60 minutes to get to the capital city. If you are traveling from the states or europe, you won't be able to get direct flights to Dominica so you will have to connect via Antigua (ANU), Barbados (BGI), St. Maarten (SXM), Puerto Rico (SJU), Guadeloupe (PTP), or Martinique (FDF).
Yep, you will need to fly out first to the Caribbean. St Maarten (SXM) is another option for direct flights to Dominica (via Air BVI). Another route is with Jet Blue to Barbados from New York and then connect with LIAT.
Europe to Dominica If you're coming Europe, the french islands of Martinique (FDF) and Guadeloupe (PTP) are the best hubs to choose from for flights from Europe to Dominica.