Ah, writing. A love after my own heart, and, like reading, I strongly believe it's a love your children will naturally pick up on when they see you engaging in it. We don't need studies conducted to know that children observe what their parents value and spend time on and follow suit.
Whether it's making grocery lists, To-do lists, writing to a friend, writing a story, or just writing for the fun of it, let your kids see you writing (not typing) on a regular basis. If you force it or "make" it a lesson it may not be as fun (unless your child loves to play school) but incorporate writing into your daily life, and they are sure to follow the interest.
My kindergartner already knows how to write all her letters and can spell some words independently and for the rest she asks me how to spell the words she wants to write as she goes. People ask me "how" she is advanced, but it's nothing I've done, she naturally excells in this area because she thoroughly enjoys spending her time writing. Every day she is writing letters to friends, making grocery lists and making up stories. A lot of time with the stories she dictates them to me and I write them, but this too, stimulates her love for creating stories, writing and reading! Often she'll draw the pictures and have me write the story she makes up underneath it. Then when dad gets home from work, he reads the story to her before bed, delighting her in the fact that the story she made up really can be read, letters make words, etc. When a third person who wasn't present for her telling it can know what it says... the magic of the written word is an adventure that, if lovingly encouraged, will hopefully never leave your children.
Here are a few more tips I can offer in the way of encouraging, depending on the age of your kids.
Find them a pen-pal or two, or three... kids love getting and sending mail, and you can teach how to address an envelope and stamp it while you're at it. This also begins opportunity to teach them grammar and how to properly start and end a letter. You can even decorate a special box for them to keep their stationary, stickers and letter/card creating supplies in. A fabulous plus to this is, it also helps them foster and grow in their friendships with others.
Don't be worried about size and capital or lowercase to start. Give them a chance to explore and gain confidence. Penmenship develops more and more with practice.
Give them LOTS of time to free draw, free write and create without you hovering. Unless you're making thank you notes, simply wait until they ask you for help on spelling what it is they are writing.
Use writing time combined with reading and penmenship practice. Index cards are excellent because it's fun for kids and they can create their own vocab flashcards. I usually write the word first on an index card and let her copy it on her own on as many cards as she needs to practice with.
There are literally countless workbooks out there for both handwriting practice and story creation, writing skills, etc.
At the Dollarstore, we found a great dry-erase board with a manuscript book on top which is great because it gives practice for writing upper and lower case letters without using up paper and it can travel well in the car. My daughter loves it and even my toddler likes to practice doodling with it, and doodles, as we all know, is where it all begins!
Give plenty of notebooks of all shapes and sizes, and encourage older kids to start a journal they can write and draw in, give them fun things to decorate it with to make it their own. Take what they already love, like nature or playing spies, and find a way to incorporate writing into it, such as keeping a nature journal or writing out their top secret spy plans and making lists of new equipment they'll need on a mission.
This Christmas we have an electronic phonics game we're giving our daughter that lets her practice writing upper and lower case with a pen on a screen pad, like a portable video game with different game modes on it, which I know she'll love... on sale it was $10.
If it's story-writing you want help in, don't be afraid to get them started if they need help. Try cutting out a few pictures from different coloring books or magazines and asking them questions about what they think the characters may be doing, or how they might meet. Then start jotting down what they tell you and show them how creating their own stories can be silly, adventurous, exciting and fun! During this process you'll also be teaching them the importance of story elements, such as characters, sequence, conflict, climax, and end. Let them create their own heroes or take their favorite heroes on new adventures! The possibilities are endless. Have fun!