On Design Sponge just now I saw a video made by iron purveyor Rowenta starring Lotta Jansdotter, an artist and textile designer based in Brooklyn. In it, she offers a tutorial on an incredibly simple method for printing cloth right at home-which would actually make an excellent DIY project to tackle with your kids.
All you need is a potato or two, some ink, cloth, and an iron. Halve the potatoes, which you'll later use as stamps. Run your iron over the fabric to create a smooth surface-you want it to be nice and even before you start printing. Next, apply ink onto the cut side of the potato, and press firmly onto the cloth. Repeat as many times as you like, and don't worry at all about making things symmetrical. Little ones are great for executing this step, as Jansdotter's adorable 3 year-old son August demonstrates in the video. Later, once the fabric has had a chance to dry, iron it again-the heat helps set the dye. You can use the material to stitch a basic a shopping tote, as Jansdotter does, or if you're not that sewing savvy, you can try this with a solid premade bag, cushion, or tee.
Go to Design Sponge to check out the full video.