Get the basic information from the page: key and time signature. Knowing what key a piece of music is in tells you which notes are part of the scale (you will rarely sing a note that doesn't occur in that scale). The time signature, which consists of two stacked numbers at the start of the piece, tells you how many beats are in a measure and which kind of note counts as one beat. One other relevant piece of information, the tempo, is often given in Italian at the top of the page.
Run through the rhythms of the piece. Different types of notes indicate different lengths of time that the note should be held before singing the next one. Once you're familiar with this notation, try clapping all the rhythms in the piece to get comfortable with the pacing of the song before you add the element of melody.
Identify your starting note. Ideally, play the first note of the piece on a piano or any available instrument that is reliably tuned. It might be helpful to sing this note on the syllable "ah" a few times, and even sing through the eight-note scale that starts on this note. Have this scale in your mind as you begin the piece. Remember that the position of that first note on the staff is usually the tonic in the scale --- the "home base" in the piece. Every time you see it, refer to that memory of the starting note.
Read in intervals from the starting note. The easiest way to start singing the correct notes in a piece is to know the relationship between the new note and the last note you sang. In general, each line and space on the staff represents a whole step, although the intervals will vary based on the key signature of the piece. Get familiar with the sound of different sung intervals --- particularly a half-step, whole step, third, fourth and fifth. There might be times when the next note makes a big interval leap, but usually you are safe reading and singing from one interval to the next.
Read the lyrics. The syllables to pronounce will fall directly under the notes on which they are sung. Remember to follow the repeat signs (two stacked dots), which refer back to the starting point of a new verse or repeated chorus. The lyrics of the new verse will be directly beneath the previous verse, so be sure to stay attentive and keep your place.