Animator has, in my opinion, one of the best vertex modelling engines of any 3D animation package, and puts many professional packages to shame. In fact, many animators who work with Maya, 3DS Max, Carrara etc. create their wireframes in Animator and export them, myself included. The point edit mode allows complete control over the position of each vertex point and its relationship to other points, and there is a comprehensive tool kit for manipulating them. With this level of control, virtually any model can be created, the complexity and scale being limited only by the imagination, skill and patience of the artist.
Often a model can be started with a simple shape, either a primitive (cube, sphere, etc.), an extrusion from a spline, or a lathed spline (a curve rotated around an axis, like clay on a potters wheel). These basic wireframe models can be added to, manipulated, altered, mirrored, joined etc. to create very complex wireframe models. My suggestion would be to have a quick read through the manual (it's tiny, relatively speaking. Compare it to Maya's, or Carrara's manuals!) and then experiment, refering back to the manual as you need to. Also, do a Google search for tutorials, they don't necessarily have to be Anim8or specific, the basic concepts generally translate across all vertex modellers.
There really aren't any shortcuts to making good models, other than pinching somebody else's work, and how satisfying would that be? The methods used to make, say, a human face in Animator are basically the same methods used in Maya or Lightwave. The big difference is that Anim8or is free, easy to learn, and has a very low impact on your computer's resources. The big pro packages are none of these things. The most important tools you need to build great models are imagination, patience and dedication, the software is far less important.
