What exactly is the job description of a scene designer?

Answer 1

Production Design is a very challenging, creative, and rewarding pursuit, the details of which can be seen at :
http://en.wikipedia.org/wiki/Set_designer
and
http://www.aact.org/people/setdesigner.html

Answer 2

As ever ... it depends on the show.

Is it a New Work or a Classic?

A scene designer (set designer) takes the script and imagines the physical aspects of the show in light of the directors concept.

This person might design models, draw sketches, draft in scale, provide plan and elevations .... and might even do the painting!

Answer 3

You mean set designer.

You should start out setting up shots for a photographer, find out if you like it.