If pottery, ceramics, or polymer clay don't seem to do it, homemade doughs and clays are a great way to play with squishy stuff, use your collective imaginations, and barely feel it in the pocketbook.
Here's a simple recipe for an edible salt dough: Add two cups of salt to two and a half cups of boiling water, then stir the liquid into four cups of flour in a big bowl. Knead on a floured board, shape, and bake for two to three hours in a 250-degree oven. Check often after two hours and bake until just slightly golden. Cool thoroughly, then paint with acrylic paints. Seal with an acrylic spray sealer.
This is a kind of bread dough recipe that's only one of many that can be used for modeling. These doughs can be shaped, molded, embellished, baked, and sealed, and form the raw material for all kinds of inventive crafts products.
For more recipes for clays and doughs, get yourself a copy of Mudworks: Creative Clay, Dough and Modeling Experiences.
Once you've got your dough made and you're satisfied with the consistency, you can use a variety of techniques to shape it. Here's a list of ideas you can use with dough or polymer clay to get interesting patterns, shapes, and textures:
Look for small and large cookie cutters (especially the small ones generally used for garnishes). Use them for cutting out uniform shapes.
Reexamine your everyday kitchen tools. Garlic presses (holes vary in size) are great extruders for making hair or just thick strands. Graters and meat mallets can be used to create textures. Walk around your house and look for other everyday objects that you might be able to press into your clay to give it an unusual texture.
Collect some items from nature – a few simple flowers, some leaves, an acorn-and examine their parts. See if you can duplicate them in clay or dough and assemble them. Try copying them first and then improvise.
Do the same thing with fruits and vegetables (try larger foods with smaller children, smaller foods for older ones).
Try duplicating different shells. You can look at pictures, but it's easier if you work from the real thing so you can hold it in your hand and look at it from all angles.
Try using different makeshift tools (toothpicks, skewers, the tines of a fork, an old toothbrush) to create lines and grooves in your clay.
Experiment with making textures. Pull netting tight over a piece of dough or clay and see what it does. Try a piece of discarded pantyhose. How about cheesecloth? Wire mesh? A cheese grater? What happens when you pull it harder? Lighter?
Try using a real leaf (wash and dry it first) as a template on some thinly rolled clay or dough. Put some waxed paper over the leaf and roll over it to make an impression. Use a knife to cut out the edges. Remove the leaf carefully.
Make braids with long "snakes" rolled out of dough. Use just two strands, then three. Braid them first and then twist the braid. See what happens.
Make some flat, wider strips of dough and see if you can weave it so it looks like a basket. What happens when you use different widths? Different textures of strips?
Use objects like bowls or baskets and form the clay over them, then peel the clay off carefully. Layer small pieces of dough or clay formed into shingles or petals to create depth and texture. Use a flat shape as your base. For example, try making a roof on a house using individual shingles, or a wreath using individually shaped leaves.
There are punches and stamps used in leatherwork that make interesting designs. (Make sure the leatherworker says it's okay to use them though!) Broken jewelry findings make useful impressions as well. Try different objects and see what you get.
Concentrate on one shape (a star or a heart, for example) and see how many variations in texture or decoration you can come up with. Create a sampler and either hang your variations as ornaments or mount them on a board and frame them.
If you just want to get your feet wet without spending a lot of money on clay, start with The Incredible Clay Book by Sherri Haab and Laura Torres. It comes with eight pieces of clay, one ounce each. Suggested projects include finger puppets, dinosaurs, beads, and more.
For more ideas, see Crafting with Clay: Clay Projects.