Begin by researching a little about jazz singing and famous jazz musicians. Learn the history of jazz to help you get into the spirit of music.
Listen to older recordings of some of the great jazz musicians. Ella Fitzgerald, Billie Holiday, Sarah Vaughan, Diana Krall, Nat King Cole and Tony Bennett are quite famous, to name a few. Study their style and the way they blend and fuse with the music they're singing, but never overpower it.
Visit a jazz club and listen to some live jazz singers. Note what you like about their style and things that you'd like to integrate into your style. Think about issues like breath control, tone and their ability to improvise.
Pick a song to memorize and listen to it a few times all the way through without attempting to sing with it. Pay attention to the music and then sing along with the song. Keep your voice smooth and your style true to yourself and unique.
Learn how to count rhythm as best you can and learn some improvisation techniques by listening to jazz greats. Know to listen to the music if you get lost especially when playing with a live band. Pay special attention to the drummer and tap your foot or something else to keep time.