Look at arrow / vertex graphics examples in the Mathematica book. putting arrows on things or showing vector fields is exampled.

Precession, minus some tedious calculous representation, is extremely simple to represent.

Arrows are tangent to the cone (due to spin). Because the spin isn't perfect and because there is some down arrow (due to natural instability of a small base, a tall neck, and wide top).

The top begins to fall just as if it were not spinning at all but because of the forces of it's spin it does not fall quickly, it falls slowly and the direction of fall "walks around" with the spin. so if it's fallen half way down and the top still spins, the result is the top "walks around" the center trying to conserve the energy of the spin (which looses, eventually g pulls it all the way down).

The two arrows were tangential and downward (plus instability that is not represented).

The resulting arrow is tangential and a little downward. If I remember correctly :)