Hi Julie,
Getting a job on Antigua if your a foreigner can be tough, there is high unemployment on the island and the government is insisting that local people are employed before considering a foreigner.
Your unlikely to be granted a work permit unless you are sponsored by a company or you are starting a business and going to employ local people in your business.
Unless you are highly qualified in a needed profession you're going to find it hard to get a job. Also if your here on vacation and job hunting you're unlikely to be chosen by an employer because your not settled, possibly not what you want to hear but true.
How did I get a job? Well I moved from the UK and bought a property but a rental would be fine. Basically the employer wants to know you are settled on the island and have been living here for a while so you know what you're getting into.
If you can tell your prospective employer you have accommodation and have been living here for a few months he will feel more secure that your not going to run off home the first time things get tough.
Next prepare your CV or Resume' and make a list of perspective employers, then go in person and ask to see the head of HR and hand them your resume', post it and it will either end up in a pile or in the bin.
if you get as far as an interview its just like an interview in any country, conduct yourself professionally, don't make derogatory remarks about the country and above all you have to convince them you are committed to staying on the island. Remember they are going to have to go to the hassle of getting a work permit for you, if they think you will pack up and go in 6 months they are not going to recruit you.