We just did Anguilla Dolphin Encounter thru RCCL on Freedom of the Seas St Maarten call 4/24. I think it's the same operator, as we had Carnival people with us. You have to take a 45 minute or so boat ride across the Anguilla Channel over to Anguilla (and fill out a customs form). Beer and soda are available for sale on the boat ride.
Then it's a very short bus ride to the beach. The dolphin program there was a lot of fun.
If you select the 'encounter' option, you get to stand in the water on a submerged dock in groups of around 10-12. The trainer will have the dolphin swim by a few times so you can 'pet' her as she goes by. Then each person will get to do 3 different interactions. a "kiss" (hold the dolphin's nose up to your cheek), a "dance" (hold the dolphin's fins like hands), and a "target" (hold your arm out high and make a fist and the dolphin will swim up and put her nose to your target).
Those that buy the 'swim' package get a couple extra maneuvers. One is the dolphin will flip over on her back and let you grab her fins and she will pull you thru the water for a bit. The other is the 'foot push' where she will put her nose under your feet and push you thru the water. There may have been a 3rd move that I didn't notice.
Before/after your group is in the water with the dolphins you can hang out on the beach, which has a shaded area with chairs.
After everyone is done you get back on the bus to the operator's headquarters where they will serve a burger/chips and punch. Liquor items available for sale. There is also a gift shop and this is where you can buy pictures (they do not allow you to take pictures of the encounter)
The pictures are $30/each (delivered on a CD) or there are packages to get all the pictures of all the interactions for everyone in your party (for 3 people it was $139).
We did the 'encounter' and were happy with it. The 'swim' looked very cool as well. The pix are spendy but what can you do.
Hope that helps!