Turn on your background track or give a signal to your background player(s) that you're ready to start.
Listen to the beat of the music to get an idea of how fast to sing. Pay careful attention to the pitch around which the song seems to be based—this pitch is usually found in the first chord and will help you find your starting note.
Begin singing at your appropriate entrance. The way you sound to yourself is not the way you sound to an audience because of the way the sound waves your voice produces interact with the bones and tissues of your face, neck and ears. Because of this phenomenon, listen to the accompaniment and rely on that as a reference for pitch. Sing with less volume than you initially think you need and sing to your accompaniment to do this.
Concentrate on how each pitch feels as you sing it with the accompaniment. Rely on this feeling to place future pitches instead of just your ear, since it's acoustically impossible to hear your own voice accurately.
Continue to sing and move your voice up or down to match the pitches in the accompaniment. When you are in tune, the wavelengths of your voice and the accompaniment should match up. This makes it seem as if the accompaniment has risen in volume and your own voice has "disappeared." Check this on longer notes. Relax and let your voice vibrate with some vibrato once you're confident of your pitch placement.