I feel that I must start with the warning that this craft project involves a needle and is not recommended for kids who can be trusted not to hurt themselves with said needle.
Now with that out of the way, cross-stitching can be a fun and enjoyable activity for all ages from kids to adults. And for people who feel that they are unable to sew, cross-stitching can be relatively easy.
I recommend investing in an embroidery hoop, maybe even a couple if you decide to make this a long term hobby. Different size loops are needed for different size projects. Here is a link on how to cross-stitch.
There are many different patterns available for purchase but there are some free patterns available online. Below is a list of some of those links, both free and for sale.

• http://www.alitadesigns.com/cross-stitch/patterns/kids.php
• http://www.freepatternsonline.com/
• http://www.stitchwitchcircle.com/