Also, don't be discouraged if they aren't singing loud. Our pop culture has elevated loud, belting voices as the norm for kids (I call it the "Annie" syndrome) but the true child's voice is much softer, and is a "head" voice, not a "chest" voice. I agree with much of the above, and suggest you talk to a local choir director, sit in on their children's choir rehearsals, and listen to some recordings of children's choirs.
The self-consciousness factor is a biggie. I sometimes have to do a real pep-talk about all of us joining in, supporting the "team", the courage that we will all feel if we hear the singers next to us, the joy of the experience of singing together, etc etc.