Fly into St. Maarten (airport code SXM.) From there, you can travel to Anguilla via air or sea!
By air: Take a 7 minute flight on Anguilla Air (http://www.anguillaairservices.com/) from SXM to AXA.
By sea: There are a variety of privately owned sea shuttles as well as a public ferry that run several times daily from SXM to AXA. Here are a few: