What will it be made of and how will it work?

I found this from Wikipedia. It seems pretty informative and seems to answer both your questions. Those external links seem pretty helpful in answering your question more, too. Try this, too, for more description.

Your first question answered- "the elevator would have to be built of a material that could endure tremendous stress while also being light-weight, cost-effective, and manufactureable. A considerable number of other novel engineering problems would also have to be solved to make a space elevator practical. Today's technology does not meet these requirements. However, optimists say that we could develop the necessary technology by 2008".
And fairly detailed descriptions of the parts involved that would make up the elevator. It explains that a cable made out of Carbon nanotubes may be the best answer.

Here's how they'll build it.

How's that in answering your question?