First, never push your kids to sew, instead, try showing them an awesome (but simple) project. This could be a little bag to put toys in for the car, a pillowcase dress or even a little quilt. It is important that they feel this is something they want to do, otherwise they will look for ways out and this can be frustrating.
Second, do not start too young. My daughter is now five and is really enjoying sewing this year. Keep in mind, she sees me sew everyday so she already understands the safety aspect to sewing. When you start too young, it may not turn out and could discourage them for a long time following.
Third, sew in short intervals - do not try to finish the whole project in one sitting. I learned this when my daughter learned to read. At first, we were always "sound it out, sound it out'..that didn't work. What did work was reading extremely simple books, once a day, fly through it, and build confidence. Over time the books increased in difficulty, but very very gradually. Now my five year old reads confidently and doesn't mind having to stop, sound it out, struggle a bit and then keep going. Sewing is the same, her first sewing experience was maybe 5 minutes, then it moved up over time. Now she can sew for a couple hours without getting bored.
Fourth, show off the finished project to as many people as possible. My daughters first very simple small quilt was brought to the local quilt shop, where they 'oooed and awwwed', really making my daughter feel special. Another tip that goes along with this step is only purchase the materials you need for each step, then as its completed, go shopping for the next few supplies you will need. Kids loving picking out things and it is a great way to turn a simple project into a meaningful one.
Fifth and most important tip... DO NOT BUY A CHILDS SEWING MACHINE. I have bought a couple and I can honestly say they are wastes of money. I would highly suggest you skip the toy/child sewing machine and buy a low level Brother or Singer from Wal-Mart. The last thing your kids need is to be frustrated at broken threads, tension problems ect. It is so much better to teach on your machine first, then once they can sew alone, invest in a starter machine for them.
My daughter Chloe recently made 2 quilts - all by herself. I started with a pile of 6inch squares of
many different fabrics, Chloe selected 16 she wanted to use, then she arranged her pattern of patches. I then took the patches,pinned them together and drew a pencil line ont he 1/4inch seam mark. This way Chloe only had to follow the pencil line to know her stitches were good. It was a great teaching technique because when her stitches did stray, she could see that, and we would take those stitches and she would fix it.
Chloe made one quilt for her little sister, and one quilt for our baby quilt charity here in Ottawa. I quilted the one for the hospital and Chloe quilted the one for her sister. Chloe loved using all my decorative stitches, doing an envelope style binding, and picking super contrasting bright thread. She even selected fabrics of her sisters favourite character - Elmo.
I feel I have taught my daughter the value of homemade, living a less commercial life, and the value of giving and sharing. For now though, she just thinks we are playing with fabric!
I hope this is helpful for you and your little sewists!