Cruise ship. That's the easiest way. Carnival-owned ships stop there.
To fly to Grand Turk, try American Airlines from Miami or Jet Blue from New York (about $450 round-trip) to Providenciales. Then take a 40-minute puddle-jumper on Air Turks & Caicos to Grand Turk (about $180 round-trip).
From a cruise ship, take a taxi for $5 to town or negotiate with a taxi driver for an island tour for about $60. Do not miss out on the water-related activities. If you are a good swimmer, take advantage of the snorkeling or scuba diving. Beginners can try the stingray adventure offered through the cruise ship.
If you are staying on the island, get your resort to help with diving, snorkeling or other activities. The island is so small that it's easy to get around.
Divers, try the Bohio Dive Resort on the beach. Very nice off-season packages include seven nights' lodging, dives, breakfast and lunch and round-trip flights from Providenciales to Grand Turk: $1,525 for a diver and $1,100 for a non-diver (www.bohioresort.com/stay-all-inclusive-packages.html).
Osprey Beach Hotel is in Cockburn Town on the beach. Pretty pool/dining area, and good off-season rates - a beachfront king room is $165 a night (www.ospreybeachhotel.com).
Turks & Caicos Tourism: http://www.turksandcaicostourism.com