To learn how to UV map, let's put a teapot in Blender. Today, this will work pretty well, but normally a teapot wouldn't fit in a Blender.
You can download Blender at blender.org. While there, I highly recommend the tutorials on the site at bit.ly/BlendToots. Packt also has quite a few good books on Blender. You can find these at: http://bit.ly/BlenderBooks. You might be a little confused or frustrated with basic cursor movements, and selecting if you haven't been through these tutorials; seeing an animation of the cursor moving helps more than writing about it would. In particular, please watch the cursor selection tutorials under Getting Started at: http://bit.ly/BlendStart.
To start texturing, we will use the venerable Utah teapot by Martin Newell. It is one of the more famous "test models" for computer graphics. This is the original Utah teapot, currently on display at the Computer History Museum in Mountain View, California (courtesy of Marshall Astor):