The teapot, is the legendaric model, not the original a replica, of one of the first real renders. This is nowadays widely used, as a model to test render, or trying to compile objects ingame.
Rowleybob:
What you are doing wrong is using splines, offcourse you could also do this, but splines work on a different way then vertexes and polygon modeling.
With splines you draw a outline of you model, starting with one spline and adding extra splines to it making up the shape.
example:
http://img288.echo.cx/img288/51/wip42fx.jpghttp://img198.echo.cx/img198/9481/wip38kb.jpgAs you can see it works different, when you got your splines drawn you need to add a surface modefier, this will create the polygons between the splines. Your splines need to form quads if you want the surface modifier to work.
In the G-max tutorials there is a tutorial on splines, its in the robot tutorial under creating the body.
EDIT:
Here is a example in pictures of what box modeling is, this combined with poly modeling is the feature of weapon and charter design.
Follow them from top to bottom, hope that explains what box modeling means. All need are the tools:
extrude
scale
translate(move)
weld