Singing is very important, especially for children. Many times reluctant singers are more likely to sing in a group setting with other children, like a music class or children’s choir.
For at home I would suggest getting a CD of songs you want them to learn for them to listen to. The more they hear it they more they will become familiar with it.
They are young, too, and I would start simple by asking them to sing just a small part at a time. Start with simple songs and chants that are fun and may even have a game.
I teach elementary music using the Kodaly method. Folk songs and games are the materials which I use. There are a couple of ways you can teach a song. One is to have the children echo a small phrase after you, then the 2nd phrase, etc. After the song is complete, repeat singing 2 phrases at a time. Another method is to sing the song with a game, and after the children hear the song several times have them join in when they are start to catch on to the song.
Songs you may know are: Twinkle, Twinkle; Ring Around the Rosie; Teddy Bear, Teddy Bear; Bear Hunt; Rain, Rain
I wouldn’t push them learning all the words to hymns yet. Play them around the house and in the car. Just exposing them will be a great advantage in itself.