Roll a piece of clay into a long coil about 12 inches long and as thick as your finger. Make ten or so of these coils and cover them with a damp paper towel.
Using one coil, create the bottom of your pottery vessel by spiraling it around itself on a flat surface. Join the clay strips by pressing firmly and smoothing with your fingers. Turn the clay spiral over and repeat the joining process on the opposite side.
Build up the sides of your vessel by placing a coil along the outer edge of the base. Press it into place and smooth with your fingers on both the inside and the outside. When you have made a complete circle of clay around the base of the vessel, cut off the excess clay and join the two ends.
Repeat this process with the other coils until your vessel is the size you want it to be. To make a curve in your vessel's profile, you will need to vary the size of your circles. If the circles are larger, the vessel will spread out; if they are smaller, it will become narrow.
Finish your vessel by smoothing it inside and outside. Add surface treatment or decoration if desired.