First, I'd do the dolphin swim at Discovery Cove in Orlando rather than on the cruise (if that is a possibility at all). It's a much better experience. Discovery Cove is a sister park to Sea WOrld, but the experience there is very comparable to Disney--great customer service, etc.
As to how to book on your own...I started with the tourist info sites on the web for the various islands and got as much info as possible ahead of time. You can even book ahead, but be sure you will be refunded (or can pay at the time of the excursion) if the ship can't get you to port. You can also get loads of good info here.
Basically, you get off the port and go to either a special spot for the excursion or the local tourist info place. This will be made clear if you booked ahead. For instance, Captain Marvin's has a kiosk you go to. The tourist info place will direct you to taxis, give you free info and frequently discount coupons for admission to places. If it is a swimming event, go to deck 9 and get pool towels to take with you. You may want to take some drinks or sandwiches with you.
Almost anything done thru
DCL can be done cheaper on your own. DCL books thru a tour operator, then adds a surcharge for their time and trouble. Yes, it is easier to pay DCL than the tour operators (shows up on your KTTW account). And if the ship can't get you there, DCL handles your refund. However, you deal with the crowds on DCL excursions which are almost non-existant on your own, and you can save a little money up to major $ depending on your situation. THe biggest savings are with 10-11 year olds.
Kathryn