In clay sculpting you join clay to clay in many ways.
Most are very intuitive. Just stick some more clay to the nose area and press it on. No problem.
Coil built shapes are made this way as well. Just press and smooth the next coil to the last.
As long as you are working moist clay into moist clay, it should not be a problem.
If you are joining flat pieces to another flat surface, you will want to be sure of a good bond. Scratch the surface, coat one piece with clay slurry and press the two together. This will ensure a strong joint as long as both slabs are moist to begin with. Clay slurry is just clay mixed with water.
Slabs joined in this way tend to trap moisture between them. It must be dried out before firing. If it is a base for a sculpture, be sure to finish the drying by raising the base on a screen so air can get under the base to dry it further. Consider drying it in an oven on the rack before firing. Otherwise it could explode in the kiln ... at least, that's my experience. :(
Step 1: Clay Glue for Slab Work
When making sculptures from slabs of clay that have been rolled out and the edges are to be joined, a little more strength is desired at the joint.
The normal way to do this is to scratch the tho edges and apply a thin 'glue' , which is basically a thin slurry of clay. This gives the joint a little extra grip.
For larger work, where the clay is moist, a little more tooth can be had by making a clay glue using vinegar to thin the clay. This will make a stronger joint.
Step 2: Paper Clay Glue
For joining clay where one or both pieces are partly or completely dry, or where extra strength is needed at the joint, it is best to make a paper clay glue.
It is made by mixing about 1/3 wet paper fibers by volume, to 2/3 clay. Thin to make a slurry, using vinegar.
This can be kept in a container for later use.
Source of paper fibers: a little toilet paper shredded in a blender
If the pieces being joined are tiny, it is best to use a clay that has no grog in it.
If the work is very large you might want the grog. Grog is previously fired ceramic clay that has been ground and is added to some types of clay that you purchase.
This slurry will allow you to join two completely dry pieces of clay. However, the joint will not be that strong. I mostly use this method for joining a small piece on to a larger piece. If you are working a lot with dry pieces, you should switch over to sculpting in paper clay. The vinegar / paper clay glue will make quite a strong joint on dry paper clay pieces.