If you want children to write, start by reading aloud to them. Talk about what you're reading; ask questions and listen. This shows how fun it is to learn by reading, and shows what words are for. Why to read will lead to Want to read. Taking in ideas from reading will lead to output.
Small children generally enjoy writing more when they get to choose their activity. We kept scratch paper and pencils available all the time. They drew a lot; they wrote menus and letters to Grandma. Some of my children made card games; they drew the pictures and calculated the effects of game mechanics. One asked family members to be guest artists on her cards, with signatures. Another taught herself calligraphy and made tiny books for her dollhouse. My youngest son at age 5 would do mazes and dot-to-dots over and over for long periods of time. One waited until she got glasses at age 9 and then went to town. She drew a lot for about a year, then taught herself cursive and started writing novellas.
