There are 3 different places to see dolphins at SeaWorld Orlando:
-Whale and Dolphin Stadium (the Blue Horizions Show)
-Dolphin Nursery (Mom and baby dolphins)
-Dolphin Cove
Dolphin cove is where you can interact with the dolphins. There is an underwater viewing area to see the dolphins from below. As well as an interaction wall that is open all day, to everyone. At the interaction wall you can walk up and put your hands in the water. It is up to the dolphins if they want to be pet or not.
There is also a "feeding area" at dolphin cove. (You can also feed sharks, stingrays and seals/sealions at SeaWorld). Each person entering the feeding area has to buy at least one tray of food. Each tray costs $7 and comes with 4-5 fish in it. There are select feeding times throughout the day, which you can find on the back of your park map (just like all the show times). It's highly suggested to get in line at least 15 minutes prior to the start of a feeding time. They do only have a certain amount of food they sell, and when they're out, they're out. It's highly recommended that if you want to feed the dolphins, to be there at park open and head straight to dolphin cove, and participate in the first feed. It's generally the least busiest. During the feeding time you will pay first, then wait in line to be let into the feeding area. They bring big groups in together, go over a safety talk and tell you how to feed and touch the dolphins. Then they have everyone step up to the wall, and hand out fish to everyone in the feeding area. The dolphins will come right up to, and as long as you listen to the talk, they'll tell you how to insure a chance to touch the dolphins while you're feeding. You generally get about 10-15 minutes in the feeding area to feed and touch the dolphins.
There is also a dolphins up close tour that lasts an hour. It starts at dolphin nursery, where you watch the trainers do a session with the mom's and babies, and you get to help by throwing a hand full of fish in the water (only if you want to). Then you go to dolphin cove and help in a traininng session with a group of animals at Dolphin cove. It's much more informative and one on one than the feeding times. You do generally have to book this ahead of time on seaworld's website, as they do generally sell out daily.
Hope this helps!