One of the best ways to foster the love of writing in the very young is to give them a blank book, diary or journal and let them pretend to write. As soon as a child can hold a pen, he or she is ready for the first journal.
In the early stages of learning to write, a child will often make lines and pretend to write words they say aloud. Giving them a forum for such writing practice actually encourages them to learn.
The child may just draw pictures or scribble, but they're also learning dexterity, eye-hand coordination, and discovering that their imaginations translate to paper.
Parents who view this as a "waste" of paper, think again. The toddler who "finishes" an entire book and proudly shows you its contents is the author of the future. The child who is comfortable with pen and paper early on will likely fare better when it is introduced to them in school.
When the child brings the book to you, and you see lines and scribbles that are illegible, be sure to ask if the child would like to read it aloud for you. Chances are you'll hear the first draft of a future masterpiece, or at least the story of the child's day.
An easy way to pique a child's curiosity is to keep a journal yourself and let the child write in it. There's no reading your private material at this age, but children like to get "in" on what their parents are doing. Your interest in writing suddenly becomes their interest in your book. Be sure you have earmarked your journal as child user-friendly, meaning, you won't mind if half the book are lines that don't make sense to you.
As a parent, you can always keep a journal together. Add your own words to their drawings and scribbles, to help a future reader interpret what went on at the time.
The love of writing starts young just as it does with reading.