The magic date, according to the report, is 16 April 1178 BCE.
The evidence -- interpreting the darkening of the sky in Theoklymenos'
vision in Odyssey 20 as a solar eclipse (an oldie); star positions
mentioned in Odyssey 5; and the movements of Hermes (identified as the
planet Mercury) in Odyssey 5.
Some sample news links:
http://www.sciencedaily.com/releases/2008/06/080623175435.htm
http://www.independent.co.uk/arts-entertainment/books/features/the-end-of-an-odyssey--homers-epic-is-finally-pinned-down-852850.html
http://www.sciam.com/article.cfm?id=homers-odyssey-may-document-eclipse
The research has appeared in the latest issue of Proceedings of the
National Academy of Sciences of the United States of America.
Finally the assumptions on which the dating is premised -- many not
stated explicitly. This is left as an exercise for Usenet :-)