When purchasing kids snow skis there are a number of things we need to consider.
It is not the same as purchasing skis for ourselves.
Kids needs are different. For starters, (in most instances) they won't have had as much exposure to the snow and skiing as adults.
Further more they do not have the same strength as adults and therefore need appropriate skis to suit their ability and size.
A good ski store will direct you to a specific section in their store with skis designed for kids.
Kid's skis are softer and more flexible, thus reducing the pressure on your kid's legs.
They are usually shorter than the adult version. However that said, the length of the ski should be based on the ski level, therefore if you child has skied before they may be able to handle a longer ski than perhaps if they were skiing for the first time.
For younger children, you should be able to stand the ski upright and it should sit somewhere between their armpit and their chin.
This will allow them to still be able to manoeuvre around the snow reasonably well.
For those a little older, you can stand upright and they should sit around head height, somewhere between the chin and eye level.
Each brand of ski will most likely measure a different length. This is an approximate guide, so if they are 2cm taller or shorter than suggested this will be OK.
Once you have purchased your kids snow skis, get them to practice moving around in them. You can simulate the real thing in the backyard on the grass. This will not only help them to gain some coordination, it will also help them to wear in their new ski gear.