Point out the notes that make up the choir members' parts. Even if your choir cannot read music, they can learn to identify when notes move up, down or stay the same. This will help them to follow their pitches more accurately. You also can teach them basic rhythm notes, such as quarter, eighth, half and whole notes, along with various rests. Learning the rhythms will help them to sing more accurately as well.
Divide your choir into groups based on which part is being sung when you are first learning a song. If a choir member can work with other sopranos, altos, tenors or basses at first, he is more likely to figure out his part.
Play the melody line of each part individually and have that group of singers sing their part as you play. After you have played once for them, listen to it. Emphasize troublesome sections of the song by slowing down your playing and demonstrating the part vocally.
Provide your choir members with audio recordings of their specific parts. Advise them to listen at home or in the car and to practice their parts.
Divide your choir into small groups with one person representing each vocal part. Have the group sing a section of the song. This is an excellent means of checking for accuracy once the choir has been working on a piece for a while.