You board the boat on Tuesday, Friday, and Saturday for a 30 min ride over to Blackbeards Cay. You will be able to enjoy the beach after the stingray adventure, and can return at 1:00 or 4:00. If your ship comes in on any day other than the ones listed, you will need to contact them and make arrangements for them to pick you up at the dock.
You will need to email them and make arrangements for the excursion. They accept Visa and Master Card and can accept payment when you arrive. They will email you with all of the instructions when you contact them and tell them how many in your party and what date you will be arriving.
If your ship doesn't offer this as an excursion, you may want to wait until you arrive to pay. I am not sure if you could get a refund if your ship is late and you miss the boat over to blackbeards cay. From what I understand they only depart at 9:00 am.