I understand that Grigori Perelman of Russia may have solved the Poincare Conjecture (The Washington Times Jan 12'04 page 2). Would ou have some elementary references which would help me understand how one would understand the context of the conjuecture and how one might approach proving the conjecture?

Well, you can find a short Description at

https://mathworld.wolfram.com/PoincareConjecture.html

The best introductory text on geometry and topology of finite dimensional spaces is The Shape of Space by J. R. Weeks, altough the Poincare Conjecture got only a fleeting mentioning there. You may also want to have a look into K. Devlin's The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time
. (Read reviews at amazon.com. Needless to say, the books could be purchased via my bookstore.)

Other than that, there've been periodic discussions at the sci.math newsgroup. Find it at the mathforum.org.