Find vocal music with harmony lines that are simple and within children's vocal range. Two-part harmony with a soprano and alto line usually works well with young singers.
Play the music for the children and discuss how they are hearing two different vocal parts.
Play the melody on a piano or keyboard and have the children sing along once they are familiar with it. Then play the harmony line and have the children sing along with that as well. You may have to play a few measures at a time and then have the children immediately echo those measures.
Give the children their own copies of the sheet music and have them touch the notes with their fingers as they sing them. Model this yourself by tracing along with a larger copy on a visual display. Talk about how series of notes move upward, downward or stay the same.
Distribute practice recordings for your students to take home. Play the melody line for the students who will be singing melody. Record the harmony line for the students singing harmony. Then include one recording of the song that includes both lines together for each student's copy.
Practice as often as possible. Children will have to get used to singing their part while others are singing a different part. This takes time and practice.