I have drawn and painted for many years, but I noticed that no matter how hard I tried, things did not have the solid look of 3 dimensions. Lately I have had more time to dedicate to this problem, and I will share my results. The basic idea is that if you can build it, or imagine building it, you can draw it and paint it.
You can construct just about any shape by putting together triangles. To simplify matters, consider equilateral triangles. If you join 5 equilateral triangles, they have to buckle in order to join at the edges. If you join 5 triangles again and again at the outside vertices, you will end up with a polyhedron with 12 sides made out of triangles. If you join 6 triangles, they will either arrange themselves in a flat surface, or you can bend them into a cylinder. Of course, 6 triangles can also be folded in other ways, going up and down, which you can see if you join pieces of triangular card board.
Apart from triangles you can work with other polygons. Pentagons joined at the edges will curve together to form a regular polyhedron with twelve sides. Figure 7 shows another pen stroke used to model a curved surface. Actually, it is two pen strokes. First a line (it could be a curved line), and then a zig-zag. Again, your triangles will be wider when they are facing you, and narrower when tilting away from you at the edge of an object. If you are studying a curved surface and trying to plot the surface in triangles, you will find particular points where the surface buckles or folds in both length and width, and at those points you would probably arrange your triangles in a group of five. Figure 8 shows a polyhedron made of pentagons. Then, if you slice off the vertices, you get a soccer ball (or Buckyball) made of both pentagons and hexagons. You can build one without too much difficulty by joining toothpicks of exactly equal length, or pentagons and hexagons made of cardboard with edges of exactly the same length. If you can practice drawing one, you may also have a structure on which you can model a face. There are included some quick sketches here showing how I would use this technique to model an object.
At left there is a photograph of one of our musicians in the Italian Marching Band. Now, supposing I wanted to make this into a painting. One way is to do photographic realism. I could draw two dimensional boundaries of colour very accurately without considering how the thing is built. I would come up with a very nice painting that would look like a photograph, but at the end of it I would not know how a musician is built. The whole point is to draw something in such a way that you understand it, and can reproduce the figure from several different angles, in different light, with the limbs in a different position and so forth.
To demonstrate the application of this to actual drawing, I have made several sketches. In the sketches below, you will notice that I try to draw all parts of the object. I draw the arm that is away from the viewer in its entirety. This is necessary in order to place everything in the right place. If you practice, you can correctly imagine the positions of the parts of things you cannot see, but I am not that advanced. I must at least make strokes with the pen without actually touching the paper.
The paintings on left look more real and solid than the drawings, but they are actually quicker. The paint is thin so you can swish it around with your brush - I describe the techniques and paints in another article: Pushing and Scraping Paint. The thing here is that you swish the paint around for each solid shape. It is like the pen sketch above with the scribbled man. You move your brush as if you were scribbling. Start with the parts that are furthest from you, such as the arm that is partly hidden on the man's other side. Then work your way toward yourself, next doing the chest, then the arm closest to you. Then decide which side is catching the light and which side is in shadow. If you are using light paint - use your brush or a piece of cardboard to push the paint to the light. If you are using dark paint, push the paint toward the side that is in shadow.