Train at the best school available and learn your craft to the best of your ability. Consider high schools for the performing arts, acting conservatories, universities and private coaching.
Discover your weakest link and improve it. Rely solely on your strengths and you will miss opportunities. Improve your movement and dancing even if your singing and acting are excellent.
Move to New York City. Many producers audition outside of Manhattan but not all. Make yourself available for every audition and the chances of landing a role increase exponentially.
Create a support group. Acting, singing, dance and voice coaches will be valuable sources of information and encouragement along the way. Consult them regarding audition material. Choose material that both highlights your best skills and sets you apart from the competition.
Have headshots made up and resumes of your training and work. "Headshots" are 8" by 10" photos, taken in close up--literally, "head" shots. They are generally in color and must be professionally shot. Your resume should include your physical characteristics (height, weight), training, work and any special skills such as playing instruments or fencing. Staple a resume to the back of each headshot. Always have several copies with you to present at auditions.
Attend every Broadway show in town. See for yourself firsthand what is happening on the stage, who is behind the production and who you would love to work for.
Attend Equity open-call auditions. Equity is the actors' stage union. You may attend Equity auditions but as a nonunion member you will only be seen after union members, if there is time. Show up early, get your name on the list, be prepared and stay focused. Be proactive and audition often---don't expect producers to come to you.
Perform regularly. Seek out auditions at other venues while waiting for your big break. Consider Off-Broadway and Off-Off Broadway productions. Note that these performances can lead to contact with agents and casting directors who can book you into auditions for shows, including Broadway. Consider every opportunity that gives you points toward getting your Equity card (becoming a union member).
Create your own show. Wait for someone else to give you a job and you do yourself a disservice. Book a rehearsal space, rehearse with fellow actors on a set program and invite agents and casting directors.