Step 1: Gather your clay. To gather clay you must first be able to recognize it. In its dry state it may look like rocks; in its wet state, like mud. Clay deposits in streams is actually kind of hard and slippery. Easy to break, up but doesn't just easily dissolve into muddy water like regular mix of clay and silt would. If you take damp clay and push it up between your pointing finger and thumb it will form ribbons. Sand and silt will not form ribbons. How long a ribbon you can form is a technique that field scientist use to determine the amount of clay in soil. More clay equals longer ribbons.
Step 2: Gather a large flat rock and a stick and another rock with a somewhat flat bottom to use as tools. The large flat rock needs to be more than a foot in diameter. A flat piece of metal if you have it will probably work even better.
Step 3: Allow you clay to dry. This is accomplished by breaking up the clay into as small of pieces as you can and allowing it to sit in the sun. Smaller pieces dry faster.
Step 4: Crush your totally dry clay into a powder using your big flat rock as a table and the smaller rock as a grinding tool. Remove any rocks or debris that might be mixed in with the clay.
Step 5: Now that you have your pure dry powdered clay you will need to re-wet it. Do this slowly adding a little water at a time until the clay is thoroughly wet but you only want to add just enough water to accomplish the task. Water shouldn't be running all off the flat rock (table in streams). Avoid folding or poking the clay to avoid creating air pockets and bubbles to your clay.
Step 6: Make a clay ball out of the clay. Then flatten it out on the rock/table. This will be the base of your clay pot so make it the appropriate size for your pot.
Step 7: Now roll the remaining clay into a small ropes. Use these ropes to make rings that you stack on top of each other to form the walls of the pot. Rub and smooth each clay ring so as to blend them/join them together so that they form one wall and not separate rings. Add very small amounts of water if necessary.
Step 8: Fire your clay pot. Make a fire under and around your pot to fire it... dry it... cook it. The actual wood of the fire should not touch the clay. Set the clay near the fire and allow it to slowly warm up. Move the fire out into a circle. Move clay into the center and after awhile start building up the fire and pushing the coals right up next to the clay. Get the fire really going and then just allow itself to burn out and cool down naturally. No hurry. Now wash the pot of ash inside and out. A cup of boiling water helps with the inside of your new clay pot.
If you have problems with your clay shrinking or cracking you can add small amounts of sand as a temper material. Start off using none as there is likely to already be some in your collected clay. If you experience problems, then simply start over again. Just dry, pound and you are back to square one, ready to begin again.
Also when firing your clay you want temperature changes to be slow. Quick changes can cause cracks and chips.