Get involved with theater productions in any capacity if you have not already done so. You need to become familiar with the presentation of a play to distinguish between productions that demand a flamboyant design versus those that are more subtle. Take any backstage job that is available, and talk to lighting designers, set dressers, prop masters, and other behind-the-scenes people about their contributions to the production.
Pursue a degree in costume design to help you to land internships and assistantships with a theater so that you can learn from professional designers. Consider taking art courses and sewing classes to perfect your craft.
Apply for a position as a costume design assistant for a theater. Such jobs allow you learn the craft from a mentor as you hone your capabilities in sewing and handwork. Build a reputation at the theater for being punctual, creative, and hard-working by taking any job given to you.
Take on costume design for a regional theater after you have shown them that you can design and put together costumes for multiple types of plays. Keep perfecting your craft by studying time periods and art history, which will help you work with directors to create an authentic look for any type of production.
Apply for costume designing jobs with off-Broadway productions after you've built an impressive catalogue of work from regional theater. For interviews, make sure you bring in a portfolio of the best costumes you have done, and make sure to have references from people with whom you have worked.
Work with off-Broadway company and create costumes well-matched to the respective plays. As you continue your employment with the company, keep your eyes open for opportunities with Broadway productions.
Try for any jobs with Broadway productions that inspire you. Do not take on a play for which you cannot create quality costumes. Keep showing the Broadway world that you have the talent for designing costumes, and develop a name for yourself. Be consistent, easy going, and most importantly, passionate about your work.