As it is a relatively small teritory, Anguilla is not particularly generous when it comes to work opportunities for foreigners. As a general rule, as long as you posses a skill that is not common on the island, you will be able to find a job faster.
People with training in IT and computer science have higher chances of finding a well paid job faster, as this tends to be a skill many Anguillans tend to lack. Health care professionals are also high in demand, since there are no teaching hospitals in the terittory. In fact, most doctors in the region originate from North America. The captive insurance industry is currently the best developed in Anguilla, so if you have any experience in this field you could find a job. The tourism and hospitality industry is also developed, meaning that a foreigner has a higher chance of finding a job in this sector. To check for jobs listings in Anguilla, you can visit the Anguilla Government official website.
Anguilla has gained a reputation for being a tax haven, so opening your own business is always a valid option, worth taking into account. Finally, you could also attempt working on online. Not paying an income tax should make it worthwhile.
You will need a work permit in order to hold a job in Anguilla and your employer should apply for one in your name after deciding to hire you.