Scientists are a smart lot, and oceanographers are no exception. The bare minimum requirement for getting your feet wet is a bachelor's degree in something ocean science-y (source).
That'd be enough to get you an assistant position on a research vessel, but something tells us you're looking to conduct your own research rather than clawing on to someone else's and hanging on for dear life. That means you'll be earning yourself a master's degree in some sort of specialty like biological, geological, or physical oceanography.
The fun doesn't stop there, though. If you want the government or some universities to give you thousands of dollars, a research team, and your own ship, then you'll probably need to have the word Doctor at the front of your name. Kind of like Doctor Doolittle, only don't let anyone catch you talking to the fish.
No, this doesn't mean you'll be performing surgery on the sea. It just means that when people talk about the ocean, everyone will look to you to make sure you're nodding.