Height
One of the key determinants in choosing the length of ski for your child is his height. This is much more relevant than age because kids grow at different rates. The shorter the ski, the easier it is to control, so a very rough guide is to err on the side of shorter for younger children and longer for older children in relation to their height. For younger children, try to choose skis that come up to their chest. For older children, the length can be up to their chin or their nose.
Weight
Some ski shops and rental outlets base their estimates on weight because weight and balance are important parts of the mechanics of skiing. The rule of thumb is that if a child weighs between 40 and 50 lbs., skis about 90 cm long should be ideal (the ski industry generally deals in metric measurements). If she weighs between 50 and 60 lbs., skis 100 cm long are ideal. For every 10-lb. increment, add 10 cm of ski length.
Experience
Height and weight are two rough estimates based on a child's dimensions but that take no account as to his ability, experience and what he intends to do on the slopes. If your child is brand new to skiing, no matter what their age, height or weight, it is prudent to give them shorter skis. Different types of skiing suit different skis as well, so think about what type of skiing your child will be doing --- slalom, downhill, cross country, freestyle, etc. --- and mention that to the ski supplier.
Safety
The most important factor for your child on the slopes is their safety. Ski environments can be dangerous, so making sure she has the correct ski is important. Consider not only length but also quality and bindings. Holding on for another season before "handing down" can be dangerous. Poles and helmets should be used at all times, as well.