Learn one or more musical instruments, and stay in practice for the long term. Conductors must develop strong ears and musicality, something playing an instrument can develop.
Familiarize yourself with classic and contemporary musical theater scores. Broadway music has a certain sound, and in includes a variety of of sub-genres as well.
Attend a music school. Take music theory, orchestration and composition courses. A conductor must have strong musical knowledge. Attend classes regularly, and practice outside as much as possible. Use resources such as student productions, guest speakers and workshops, and other educational opportunities to expand your craft.
Take a directing or public speaking course. This allows you to brush up on your people management skills, a necessary quality in a Broadway conductor.
See as many musicals as possible. Observe the conductor and how he works during the show. If possible, contact the theater and ask for any opportunities to observe the conductor and orchestra during work hours. This is sometimes available to students or through an internship.
Move to New York City. Broadway productions are all located there, and so will potential work. Plan well ahead and research places to live and job opportunities -- preferably music related -- that can sustain you in your first years.
Familiarize yourself with the career ladder for a Broadway conductor, and take jobs at the bottom. Look for accompanying gigs for auditions and rehearsals, then getting last chair -- keyboard -- on an off-Broadway show. Over time, work toward moving up in the orchestra, then to an assistant conductor position.
Network as much as possible as you work up the ladder. Attend colleagues' shows, and always keep your ears open for opportunities. Talk to fellow musicians about their projects often to see whether anyone is in need of an orchestra member -- and eventually, a conductor.
Join the American Federation of Musicians, which requires annual dues. Join the local 802, the local chapter in New York City. Both organizations offer valuable resources and networking opportunities.
Stay in practice, and excel at any job you land. Like most performing arts positions, conducting jobs are landed through referral, experience and time.