I recently moved to Grand Cayman. It was relatively easy. First, get a job. Second, find a place to stay. Third, apply for a work permit with the first two (your employer will do that). Amazingly enough I ended up buying the dive operation I came down to work for 8 months later. Cayman law requires you to have a Caymanian partner who owns 60% shares in the company (not 60% of the money or profits). Buying the business was pretty easy but there were quite a few fees involved. But there is no tax (there is hidden tax like duties and stamp fees when you purchase housing and land but no yearly recurring taxes).
Grand Cayman is a very easy island to live on. English is the main language and it is very North American in terms of services. The cost of living is higher but that is the price you pay for living in the tropics on a beautiful island with one of the best beaches in the world. And of course, some of the best diving in the world as well (http://photos.seasportsdiving.com/).
I would have to say it was one of the best decisions I have ever made.
Hope this helps!