Armature
Armature is a sort of doll skeleton, usually made of wire, although you can buy armature in the form of interlocking plastic beads. Armature is necessary to give a doll articulation, or to make a doll whose head is a heavier material than its body (for example, a clay head on a cloth body). Making your own armature will require wire cutters, pliers and wire. Using plastic-covered wire will prevent steel wire from rusting and copper wire from turning green. Create the armature by making a loop for the head in the middle of a long piece of wire, then forming arms by wrapping the wire back around itself. Then, you can do the same to make a torso and legs. On top of the armature, you can add foam or paper towels and tape to form a body. Or, if you want to sew a doll body, make the cloth body and insert the armature when it's partially sewn.
Clay
There are numerous kinds of clay to work with; what you choose is a matter of preference. Polymer clays are popular. Some of them air dry, but most of them need to be baked. Another kind of air drying clay, called cold porcelain, can be made with ordinary household products. You can also use epoxy putty, which is very durable once it's cured, but can be difficult to work with.
There's a wide selection of sculpting tools you can use as well. You can get kits of sculpting tools, or you can make your own tools using wire, toothpicks, chopsticks and other things you find around the house. Most clays can be sanded after they're completely cured, but you should use a very fine sandpaper of at least 200 grit. Also, you'll find sculpting easier if you're working on top of something. For example, take a dowel and form a ball of foil on top of that. Then, you can put clay on top of the foil and sculpt the head.
Fabric
You'll need a pattern to work from, which can be found online or in fabric stores. You'll need a bigger seam allowance for small sewing; items that require small seam allowances should be hand sewn. You may occasionally need to use fabric glue, but it can discolor fabric, so test it on a piece of scrap material before you use it on a project; the same can be said of Fray Check. Natural fibers like cotton, silk and fine linen will yield better results than synthetic fibers. This is especially true for doll clothing, because natural fibers will hang much better on a doll than synthetic fibers. Sewing small items with a sewing machine can be made easier with a lightweight stabilizer, which will keep the fabric from getting caught.
Other Ideas
You can paint on both clay and fabric, but you'll need less paint if you buy colored clay. Use oil paint, watercolor, acrylics or latex paint, although some of these will need to be thinned. Other methods of adding color include watercolor and fine-point markers. You can even apply makeup powder to dry clay with a napkin or cloth if you use sealer on it afterward. Doll wigs can be store bought, or you can make your own. Miscellaneous items that may be useful or even necessary, depending on your project, include a hot glue gun, pins, a rotary cutter and fabric scissors.