I have made a small tray with my granddaughter Anabel. We did not make any pattern all she did was pasting the tiles to a tray in a simple checkered pattern. It is surprising how well it actually came out. We also did not do any grouting in between the little tiles and she simply pasted them as close as possible to each other.
For kids this one of the very good mosaic ideas for beginners. It is hard enough for a little kids to apply the glue and paste the small tiles next to each other so it is very good exercise for those small motor skill.
Other possibilities are to get some of the many kits available. You will also be able to get kits that use paper to make the mosaics. I think that is also a ery good idea as the stickers are a lot easier to apply for the little ones.
Once the beginner is comfortable with the mosaic ideas for beginners, it is time to move on to the "real" thing. To learn all the techniques it is a good idea to get a good book with mosaic instructions.
You can go to Mosaic Crafts For Beginners for more easy ideas. There you will find a craft using pumpkin seeds that is a whole lot of fun to do.
Go To: Mosaic Crafts For Beginners