Qualifications
Becoming a captain on any ship will take a lot of work. And if you want to command a Coast Guard or Navy ship, you've got a wee bit more to do.
In that case, you first need to be a commissioned officer in one of those services (which means you've done an ROTC program at college or have studied at the academy), then work your way up through their ranks. Make no mistake, it takes years just to even get in line for that kind of promotion (source).
If you want to command a merchant ship, there's the U.S. Merchant Marine Academy located in Great Neck, New York. It's one of the five U.S. service academies, and while it can lead to commissions in the Navy and Coast Guard, it typically prepares young midshipmen for careers as merchant marine officers.
If you're interested in the cruise line route, already having a background in ocean travel of one kind or another wouldn't hurt, but it isn't essential if you're willing to get in on the ground floor. You could work as an apprentice alongside captain and crew.
As far as fishing boat captains go, here too you're going to need some years of experience under your belt before you get to set sail while sitting in the comfy captain's chair. Even if you're starting out with your own personal vessel, without an experienced captain and crew, your odds of making a living—or even coming back alive—aren't something we'd take any bets on.
Finally, you can go about it the old-fashioned way, Mark Twain-style: get yourself hired on as a deckhand on a Mississippi River barge, gradually work your way down to Louisiana, and see if a shrimping boat will take you on. Then, work your way through several positions on several ocean-going vessels, learning everything you can and saving every dime you can until you can afford to buy your own boat.
And get used to gumbo, because you'll be eating a lot of it.