Wedging clay is a hot topic to discuss among potters. Some believe that spiral wedging is the best way for preparing the clay, while others will not even think about moving away from the bull's head or ram's head wedging technique. Some ceramic artists even differ about the spelling of the wedging technique - is it bullshead, or maybe bull's head or even just bulls head - and the same argument is used for the ramshead method. Then we also have other techniques like slam wedging and there may be more, but we will discuss that later.
Most potters agree that proper wedging of your clay is a very important part of any clay work. This is how you can get rid of air bubbles in the clay, but it is also a way how to recycle your old clay. Kneading is another term that is used often. Pushing clay through a de-airing pugmil is also considered as a way of wedging in modern times.
Some ceramic scholars learn that a chunk or block of clay is cut into two pieces with the shape of a wedge. The top one is lifted from the lower one, turned over and slammed onto the wedge that remained on the wedging table. This process is repeated until there are no more air pockets in the clay.
Kneading follows the wedging process to get the clay uniform in plasticity, texture and color. Some potters believe you have to count the number of wedgings or kneadings, and some who are long time in clay say they feel when the clay is ready.
As long as you remove all the air pockets or anything that may mess up your wheel throwing or handbuilding process, then you should be safe to proceed.
In the picture on the left, coloring was used to show the movement of the particles during wedging. It may be an interesting and stimulating test for you to see what happens after 10, 20, 30 times and more of wedging your clay.