If you want a close encounter with dolphins on the Big Island, there are several possibilities.
You can sign up for a snorkel tour in Kona and hope to find a pod of dolphins. Many snorkel tours will stop the boat and allow snorkelers to swim with the dolphins if they encounter a pod.
You can snorkel on your own off the Kailua Kona pier and hope to find a pod of dolphins. It does happen on occation, but usually when you least expect it.
The other option is to sign up for Dolphin Encounter at the Hilton Waikoloa Hotel. If you are interested in the Dolphin Encounter, contact the Hilton in advance of your trip to make reservations.