Start with a daily vocal warmup. Practice singing "hmm" by starting on a low pitch and gradually increasing the pitch. Complete this exercises on several different pitches to warm up your voice. This exercise should be used before singing any Broadway song.
Vibrate your lips by making a "brrr" sound. The lips should be buzzing but be loose enough to flap a little. Again, complete this exercise on several pitches. This will help you build strength in your voice to prepare you for Broadway music.
Sing scales on solfege syllables. Use a piano to play C. Singe a major scale on C with the solfege Do - Re - Mi - Fa - Sol - La - Ti - Do. The corresponding notes on the piano are C - D - E - F - G - A - B - C. Continue playing each scale by transposing each pitch a half step higher. Most Broadway music uses scales.
Practice vocal etudes that will help to develop and strengthen your voice. (See Resources)
Continue each practice session by singing Broadway songs that fit within your voice. Take your time learning these songs and use the piano to check your pitches.