[edit] Steps

Sign up for a karate class. Many people think it's ok to study martial arts from a book. Not for a beginner it isn't! An authentic karate school is preferable, but the important thing is to be in a class.
Train regularly. If your class meets 3 times a week, go 3 times a week. Practice at home or in the park on your off days. Don't slack off!
Put in the time and effort. Winners do things that losers don't think are necessary. Depending on which style of karate you choose to study, there will be a number of belts you have to acquire before reaching black. Be patient, and climb up in the ranks.
Prepare to pass the test for black belt by going over everything you know and perfecting it.

[edit] Tips

Don't be lazy! If you find a way to earn a black belt in a month's time, or with minimal work, it's not authentic! Most arts require years of dedicated practice before one rises to black belt level.
Be physically and mentally healthy. Eat right, train hard, and focus on your goal.
When choosing a karate class, try to visit different classes before you decide on one. Talk to the instructor and the other students, and see if the class is a good fit for you.

There are a lot of schools out there which are a joke. Do your homework before signing up.
Depending on the style, it will probably take a VERY long time and lots of dedication to get a higher degree black belt.