Here are some instructions for making a simple, coil pot vase. A vase made this way is called a coil pot, because of the way the clay is rolled out in coils and is built up to form the walls.
Start with a small pad of clay. Using an old toothbrush, roughen the surface with some water so that the first coil will attach firmly. Most large cities have a pottery supply business located in them. You can buy clay from a supplier or you can try finding some clay in a stream bed.

Roll out a coil on the table so that it is about one centimeter thick. It's not too important how long it is. If it's too long, simply overlap the starting point of the coil and keep on going! Roughen the undersurface of the coil with the toothbrush and a bit of water. Whenever you join two pieces of clay together, wet and score the surfaces to give a better bond.

Continue adding coils. You can smooth the coil texture out with your thumb or a flat wooden tool if you wish.

As more and more coils are added, an organic, asymmetrical form will begin to develop. Experiment to see what kinds of forms you can make. With a bit of patience and practice, it is possible to make quite a finely crafted vase or open bowl with this simple technique. The main thing to remember while working is to try for a fairly even wall thickness as you coil your way around the pot.

You can create texture on the outside of the pot if you wish by pressing objects into the wall or by carving some patterns onto the surface. Once the pinch pot has dried out a little bit, it can be burnished. You can use a smooth stone or the back of an old spoon to rub the surface of the pot. The more you rub the surface, the shinier it will get.
People have been using this same pottery technique for about 20,000 years. We hope that you have some fun trying it out for yourself!