Practice with a book of rhythms. Becoming comfortable with rhythms will make it easier to perform on the spot.
Work through a sight-singing book. Practice daily; approach each melody carefully until perfected. Sight reading will become easier with time.
Start an ear-training course to train you to hear intervals quickly. This, in combination with daily singing and rhythm exercises, will help improve a singer's ability rapidly.
Start a session by looking at the key signature. It is important to know what key the music is in to avoid singing incorrect pitches.
Analyze the rhythm before beginning to sing any part of the melody. If the rhythm isn't correct, the melody will falter.
Determine the accidentals within the melody that will cause confusion. Look at any accidentals closely.
Rehearse the piece mentally. If you can't play back the melody in your mind, singing it will be even more difficult.
Sing the melody with a steady tempo. With practice, these steps will become much easier.