Take acting classes. Sign up for workshops and night classes or enroll in a full-time conservatory or university program. Take formal singing lessons as well if interested in performing in musicals. Acting jobs can require many talents.
Build your resume by performing in university shows, summer stock and regional theaters. Without a body of work to your name, it is difficult to get seen for most Broadway auditions.
Move to New York City. Unless you build an incredibly successful acting career in another major center like Chicago, Toronto or Hollywood, it is very unlikely that you will be brought in from out of town for a Broadway audition, given the vast wealth of actors located right in New York.
Get a professional headshot taken. Combine it with your resume into a submission package for auditions and agencies.
Get an agent. Talk to working professionals in your community to get referrals for good agencies that send people out to major auditions on Broadway. Some agencies only sign people based on referrals, so network with as many people as you can to get leads on good agencies.
Find your own auditions in addition to working with your agent to land major Broadway auditions. Resources such as Backstage.com and Playbill.com sometimes list auditions for shows that will play on Broadway. Submit your headshot and resume. If you've got the right combination of looks and experience the directors are seeking, you could get that big call.