Young children should start learning to "write" through narration, or in other words, talking. Ask your children about their day. Ask them for details and descriptions. Occasionally write what they are telling you. My girls wanted to write in a journal and write stories before they could really write, so they would simply tell me what they wanted me to write. They still love to go back to those first stories they created! Another form of narration is to have them retell a story you have read to them.
Narration leads to descriptive writing. Asking questions is again encouraged here as you ask them to go into detail about characters, events, places, etc. It is wonderful to have them draw pictures to go along with the words. I purchased a fun book filled with pictures you can show your child and ask them to write about what they see. This is especially helpful for visual learners.
Expository writing will naturally follow description as the previous two will help your child learn to enjoy writing. A great time to begin teaching this is around the age of 12. Once a child has learned to use exposition, they will be in a position to write persuasively. In our scholar classes, we have our youth write persuasive essays almost weekly. I have had the privilege of watching their thoughts and writing abilities grow and find great joy in reading their essays.
If we skip any of these steps, we are encouraging a hate of writing, which a couple of my children have experienced as I didn't know these principles until fairly recently. It has taken a lot of time to overcome their dislike of writing. I can't say they like it much better yet, but they are willing to try and are improving with each assignment. We should help our children never lose sight of creative writing as this will help them in all of their other writings. Many homeschool moms and students alike are intimidated by writing. If we can remember the purpose of writing is to feel joy in creating something of their own and to build their confidence, then we have accomplished something great!