The most traditional method of creating texture is with the creative application of paint. By using different paint brushes and by applying the paint on the canvas in creative ways, the paint itself creates the visual illusion of texture.
For example, if an artist was trying to paint the hair on a female subject, the artist might choose to paint the hair on in repetitive spirals, creating the illusion of the texture of curly hair.
Paint applied in thick, visceral strokes on the canvas can do more than create an illusion of texture--the paint itself becomes the texture. The works of Vincent Van Gogh are excellent examples of this technique.
Texture on the painting can begin before the paint is even applied to the canvas. If you are painting on a canvas and priming your own canvas, you can make texture through the creative application of the gesso on the canvas. By applying the gesso thickly or even by mixing an agent into the gesso (like sand), the canvas becomes a textured surface that will show through the painting. This technique is something of a risk because the surface under the painting can always threaten to take over the painting itself. If the texture under the painting is too prominent, then it can distract from the painting itself.
If the artist chooses to try this technique, it is best to begin with subtle textures.
Another method of creating texture beneath the painting is to use old used canvases that already having paintings on them. The subtle build-up of paint on a canvas creates its own textures.
Try to find alternative surfaces to paint on. An old door, gessoed paper, carpets, newspaper and other materials can provide intriguing and provocative textures that lend depth and intrigue to any painting. Be careful that you are painting on a surface that will not be degraded by the chemicals in the paints. Allowing the surface--whatever you are painting on--to show through the painting can give multi-dimensionality to the image. Painting on a surface that is related to the subject of the painting--for example, painting an image of a house on a door--gives the viewer more to think about, especially when the interaction between the painting and the object being painted on is well executed.