One great way to get to/from Anguilla is by ferry. It's easy to get to St. Martin for instance:
There are taxis outside the airport terminal, just tell the taxi driver you want to to to Blowing Point (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 Marigot, another guy will take your luggage and deliver it to you after the immigration (passport) and customs check.
This information based on forum thread:

