Skinning is editing flat images(textures) that will be displayed on the model. Imagine it as having a wooden 3D cube(that is the model), and you cover it with flat pieces of colored papers(the textures).
Despiting the textures there is also 1 more type of 'surface' you can put on model: Shader (click to read more). The use of these, however, is advised only for skinners with more knowledge.
It is important to distinguish Skinning (texturing and shadering the model) from Modeling (creating a whole new model).
What is needed to start skinning
- Photoshop/GIMP/Paintshop pro etc.
Here is a tutorial that explains best the basics of skinning: