Small children can start sewing with lace up cards. Cut it out and punch some holes around the edge with a hole punch. A shoelace becomes a 'needle' and thread. This becomes a wonderful rainy day project especially if you can find some multicolored shoelaces. When your child has progressed from lace up cards, have them sew on buttons.
Buttons are simple because the holes are prepunched and can be so much fun.
You can also teach your child to hem a simple scarf, or hankerchief. If you choose a printed material then any stitches that are not perfect will show less. Many grandparents would be delighted to recieve a scarf that was made by your child as a gift. When your child is ready to move on to a more complex project, have them make a needlebook, and matching pincushion. This could be the start of their very own sewing basket.