In Nassau The Dolphin Swim/Encounters are done at Blue Lagoon island. There are 2 choices of experience: During the Encounter you can pet, feed and kiss the dolphin while standing on a platform; The Swim with the Dolphins includes a 30 minute interactive swim where you will actually be able to spend time playing with them. Personally I don't think the Encounter is worth the money. If you really want a memorable experience, pay the extra money and do the Swim.
This excursion fills up very quickly (months in advance) - so if you have not already booked it - I would do so immediately.
You can found out more information about it at www.dolphinencounters.com
. I would also take the advice of the other posters, and book this with the cruise line. Since this is a very popular activity, when ships are in port they usually book all the available slots and there is often no availabilty for individuals to book on their own.