Start out with a love of books, information, information media, or whatever all this info stuff is called these days.
You need academic training and credentials, starting with a bachelor's degree—in anything—and, for the truly dedicated, a master's degree in library science. If you can't get enough of book learnin', you can spend many more years getting your doctorate, but that's only necessary if you want to spend your life teaching and making the lives of your graduate students miserable.
There are the specialists, though, who require a bit more schoolin'. Law librarians, elementary and secondary school librarians, and their ilk all require specialized degrees. There's law school for the law types, teaching credential school for the teacher types...you get the picture.
Some states also make librarians get certified, meaning more studying and even more tests. Getting trained is no walk in the park, but for the truly dedicated, it's all worth it. You'll become an impresario in the world of information (source).