If you are staying in one of the larger resorts, some will offer shuttle services to/from the airport. In many cases these are free shuttles and might be something you would consider taking advantage of. It is worth noting these shuttles are often shared rides. Taking one may result in your having to wait for other riders to be dropped off or picked up. If you want any extra services, like a stop at Eldon’s Grocery after arriving on the island, this may not be an option with the free shuttle.
Smaller resorts may not offer this service, but most will have some form of arrangement with a taxi provider they recommend. Fares from the airport to West End or West Bay generally will run about $25 USD.