Sign up for an acting class. If you have little to no acting experience, but think you could really have a natural talent, sign up first for an acting class. Acting classes are great because they are taught by professionals, surround you with like-minded individuals and give you an opportunity to act. See if you really like acting and can do it well. It's also important to take a class to judge your stage fright. Some people are good at acting in front of a mirror by themselves, but can you do it with several people watching your every move?
Audition for a local play. Every stage actor must start out somewhere, and usually that place is in the middle of nowhere in a part that is not large. That is OK, because all famous actors started out in the same situation. Audition for a local part in a play. Attend the audition on time, give it your best and you may just land a part (even if it's only one line).
Work your way up from the bottom and gain tons of experience. Broadway actors have been acting for years; they just aren't born overnight. Understand this and be patient. Work your way up from local plays as supporting actors to the lead role. Once you master that, apply for a play that tours the country. Once you build up a resume and portfolio, then you can apply and audition for a role in a Broadway play.
Hire an agent. While you can get to Broadway on your own, it's very difficult it not nearly impossible. Agents will take a part of your salary, but they will also help you make more money because they can actively search and find auditions and plays for you to act in. Once you hire an agent, discuss your goals and desire to someday reach Broadway.
Join a union such as Actors' Equity, the union that represents stage actors. Once you hire an agent and become serious in the role of stage acting, make sure you join a union to protect your rights as an actor and gain support from other actors in the union. Joining a union may also bump up your pay and increase your benefits. In order to apply, make sure you fit the listed requirements (see Reference below).