Are you asking how to graph an (x, y, z) point on a 2D screen or piece of paper, giving it 3D perspective from some angle, by hand?

The only truly 3D graph I know of is the universe itself--plotting a vector there is as simple as constructing an arrow, marking off measurements, and placing the arrow in the proper place and at the correct angles.

If you are indeed asking what I think, perhaps this picture will help.

The "y" and "z" axes in that picture are basically the same as the traditional "x" and "y" axes. However, the "x" axis in that picture should be seen as coming out at right angles to *both* of the other axes. You would plot a point on this graph by first locating the proper y and z hash marks (determining your initial horizontal and vertical position), and then by move up and to the right or down and to the left depending on the "x" coordinate.