After arriving at Owen Roberts International Airport in Grand Cayman you can take a taxi to where you will be staying.

Taxis charge fixed rates depending on how far you are going.  You can see actual costs from Owen Roberts Airport to most destinations on the island in the Cayman Airports Information Pages.  The prior link also includes the passeneger and luggage regulations and applicable surcharge amounts.

Hotels and resorts are not allowed to arrange their own shuttles from the airport, but you can arrange shuttle transfers in advance of your arrival either through your travel agent or through the hotel concierge staff.

Taxis can be quite expensive (although of a consistently high quality and with great service), so as an alternative many visitors rent cars. Car rental in Cayman is offered by several highly reputable and established local and international companies. As of 2014, an economy car will cost $40-50 USD per day, excluding taxes.  Various optional insurance coverage packages are available for purchase.  Some car rental companies also have convertibles and Jeep-type vehicles for a higher price.

Although some visitors have reservations about driving on the left, confidence increases after a short time. Cayman is a very friendly and relatively safe place, so if you were to get lost just stop and ask and people will happily help. A rental car is very useful if you want to get off the beaten path and visit Rum Point, Hell (West Bay), or the Botanical Gardens, which might be a distance from where you are staying. Taxis can be used for these but will be expensive.  Remember to check your auto insurance and credit card policies for international car insurance coverage before leaving home.  Additional car rental insurance may not be necessary if you are already covered through an existing policy.  The savings can add up to hundreds of dollars.