Earthenware clay is the best clay for handbuilding pottery because of its strength and plasticity. They are more forgiving than other clays. Grogged clay is also best used for hand building as it contains a high amount of alumina and silica which helps in reducing the shrinkage and protecting your piece from cracking when firing. The grog also provides strength if you are building larger pieces.
Handbuilding with clay allows you to create ceramic forms without using a throwing wheel.
Before starting to build your project out of clay you need to knead it, a process also known as wedging. Kneading clay makes it easier to work and maintains a consistent moisture. It also eliminates air bubbles that may have been trapped when the clay was mixed or recycled.
The three methods of handbuilding are pinching, coiling and slab building.
Once you have experience with these three methods, you can make just about any object out of clay. It helps to start with pinching, and build upon the technique with coiling, before moving onto to slab construction.
Yes you can using air dry clay. You just let it dry overnight instead of firing it. However, you will not be able to eat or drink out of this type of ceramic piece.
And no, you cannot use the oven to fire it ad ovens do not get high enough temperature to vitrify your clay.