Here is a quick guide to coil building. Its one of the basic making methods used in pottery.
Coiling is a way to make work on any scale from tiny up to hut-sized.
Coiling can be so versatile because it is so simple: sausages of clay are joined-on successively to grow the form. There are many variations to this technique as you'll see from the video at the bottom of the page but this is my version.
Step 1 - make a base
First make a base for your piece. If you want a narrow or rounded base then a pinch-pot is a good way to start. Alternatively, start with a thick slab of clay. It could a disc for round pots or a square or any other shape. You could even use a mould to form the slab into a bowl shape to build upon.
Step 2 - make a coil
You can make coils in many different ways. The easiest is to shape a lump of clay into a rough sausage shape in your hands then roll it back and forth on the table to make it longer and thinner. It takes a bit of practice to do efficiently. Common problems are that the coil becomes oval in section or becomes too dry and cracks. Try to roll the coil as far as possible across the table so that it does more than one rotation - that stops it going oval. Avoid lots of rapid, gentle rolling because that just dries out the clay without doing much work.
Alternative ways to make coils are to extrude them or cut them from a block. These two methods produce soft coils without the dry surface that sometimes occurs when rolling coils.
Step 3 - joining the coil
Each coil must stick well to the base or previous coils. If the joining surface is dry or firm (leather-hard) then wet it first to soften it. A well rolled coil should be soft enough to squidge on without any cracks appearing. Push the coil firmly onto the mating surface and cut it to length. An angled cut is best. Now work the new and old clay together to cover the join, both inside and out. Work rhythmically doing the same movement all the way round and your pot should stay symmetrical.
Step 4 - pinch the coil (optional)
Normally the thickness of the walls is set by the diameter of the coils. But if you want to make very thin walls then you could be adding a lot of coils to gain any height. Instead, you can if you wish, add thick coils and then pinch them down to be thinner and taller. This allows you to grow the height faster for each coil added.
Another alternative is to use straps of clay (flattened coils).
Step 5 - add more coils
Keep adding coils. You needn't worry too much about the surface finish yet, just concentrate on gaining height. Eventually you'll find that the walls are too soft and wobbly to continue with good control.
Step 6 - let it dry a bit
It may be possible to complete a tall narrow form without letting it dry a bit but any large open form will need to dry and stiffen a bit at the bottom to support more wet clay at the top. The best thing is to put the work aside and start a new one while the first one dries a bit.
Once the clay is firm enough to carry more fresh clay, keep going but be sure to dampen that dry top surface to take the first new coil.
Step 7 - Refine the shape and surface
You can beat the walls with a paddle on the outside and your hand on the inside to improve the shape so long as the clay is not too dry. You can also scrape down the surface to remove any lumps and bumps using serrated and then smooth metal kindneys. You can even use a surform blade (like a cheese grater). Having got the shape right you can pay attention to the surface by either adding or removing texture.
Western studio methods
Please remember that there is more than one way to do anything in ceramics. I don't necessarily agree with all the advice you'll see in these videos but they are useful nevertheless.
More traditional methods
Here is Maria Montoya Martinez, a pueblo potter using traditional coil building methods. I recommend fast-forwarding to about minute 2 of this film. Followed by the Japanese potter Shiho Kanzaki using a hybrid coiling / throwing technique to make a tea bowl.