It is possible to make rag/cloth doll hair out of almost anything and in many different styles.

The most popular are:
Knitting yarns/wool
Australian Yardeno Mohair
Cotton thread
Embroidery thread
Nylon manufactured doll hair
Strips of fabric
String
see links for suppliers

These are then sewn, glued or felted onto the doll's head.
NB: The American word 'bangs' means fringe.
Needle felting involves using a barbed felting needle to push the 'hair' fibres through and into the doll head.

Needle sculpture involves placing lots of stitches into the doll head and body to create more sophisticated, 'sculptured' features. A little like quilting, the stitches provide shape and texture, holding the stuffing in position to create a raised nose and defined mouth, eye sockets, chin, belly button, ankles, dimples etc.

Materials required:
It's all a matter of personal preference which fabrics, needles and threads you use for needle sculpting your doll. 
There are two main types of fabric suitable for this technique.
Tightly Woven Fabrics.
These have less stretch than the knitted fabrics unless cut across the bias. They are harder to needle-sculpt than the stretchier knitted fabrics:
Pima Cotton (combed cotton)
Calico/Muslin (use a good quality high thread count calico)
Southern Belle Muslin (high thread count/tightly woven) www.dollmakersjourney.com
Knitted Stretchy Fabrics.
Some people find the texture of some of these fabrics unpleasant to work with:
Nylon stockings
Some 'doll skin' can be slippery and shiny as well as being stretchy and a ghastly pink!
Velour - This is the thickest knit fabric used in dollmaking.
Lycra - Stretchy nylon.
Stockinette/ T-shirt fabrics/ cotton jersey knits
Doe Suede (a knitted suede which has a smooth surface on one side and a textured, fuzzy alternate side rather like brushed nylon only with minimal stretch - Not available from UK manufacturers, but considered one of the best fabrics for needle sculpting and handling).
Strong Thread:
Quilting (including the nylon 'invisible' variety), button or upholstery thread.
Fine threads such as silks, polyester sewing threads, beading threads are not so strong and may snap more easily, but give quite a professional finish.
Needles:
Fine doll needles of 3" or 3½" are commonly used. The needle needs to be fine and strong enough not to snap as it is pulled through the layers of fabric and stuffing materials.
You may need longer doll needles if you are to sculpt areas of the body.
I find my mini pliers are useful for pulling needles through awkward layers, though beware of breaking the needle. (See tools)

Methods:
One way is to apply the face with paints or pencils first, then add stitches e.g. from eye socket to base of nose and up to bridge of nose on the opposite side, then down to corner of mouth etc., much like a dot to dot puzzle. Another way is to mark out where the sculpting stitches will be made with a marker pen/ glass-headed pins and apply the face with paints or pencils once the stitching is completed. The amount of tension you exert on pulling the threads through and the number of stitches you make, will naturally alter the look of the doll face, so it may be best to make up some sample heads and practice. Try out the different fabrics and see what works best for you.

Check out some classes, videos or books on the subject, too.
(See links page). Here are just a few suggestions:
Individual doll patterns offer instructions on sculpting the body & head.

'Creating Faces. Needle Sculpting from the Beginning' by Barbara Owen. www.designsbybj.com
 'Creative Cloth Doll Making' ISBN: 1840924039 by Patti Medaris Culea
http://www.pmcdesigns.com/
'Sewing and Sculpting Dolls' by Eloise Piper
http://www.sistersanddaughters.com/books.html
Lisa L. Lichtenfels 
'Anatomy of a Doll' by Susanna Oroyan ISBN: 157120024 C&T Publishing.
Antonette Cely's video 'Customizing Doll Patterns' is available in PAL format compatible with UK VHS video machines.
http://www.cely.com
Dorit Schendzielorz' Needle sculpting Video. (You will need to check if this is in PAL format for UK video compatibility)
http://www.frontiernet.net/~dorit/video.htm

Skinning

'Skinning' involves applying PVA glue to the needle sculpted doll head onto which another layer of cloth is applied. It is important to smooth out all the wrinkles and push the top layer of fabric gently into all the valleys and dips of the face. This can be achieved with a Clover Mini iron or any tool with a small flat surface. Once you have applied the 'skin' you are left with a needle-sculpted face that doesn't show the sculpting stitches. However, there will be folds of fabric around the doll head at the sides which need to be tidied up and secured with gathering stitches and covered with the doll hair.

There is also a technique known as 'Cloth Over' which involves moulding a polymer clay face and then covering it with a cloth layer in the same way as skinning. Antonette Cely's video 'Making Faces' describes this technique and is available in PAL format compatible with UK VHS video machines. http://www.cely.com