Joe,
You have several options for finding out the details of a Tornado Watch.
As previously offered, weather.gov and spc.noaa.gov will give you good detail about tornado watches.
What I do in Jacksonville, FL is:
1. Keep your local National Weather Service office as a bookmark/favorite.
For me, it's
http://www.srh.noaa.gov/jax
That gives you an overview map, with a legend, and would highlight the counties with watches, warnings, etc.
Use weather.gov to find your local area office.
2. Keep the Storm Prediction Center office as a bookmark/favorite
That's the link (given already)
http://www.spc.noaa.gov
Here you will find details about each Watch, Mesoscale Discussion, and a Severe Weather Outlook for today, tomorrow, and the upcoming week.
Each convective watch (e.g., Severe Thunderstorm, Tornado) is issued a number. The numbering system starts Jan 1st with 0001 and continues ad infinitum.
Each watch that is issued has associated probabilities of tornadoes, hail, and wind damage.
Explore the site, it's packed full of current and archived data!!!
Also, you can look back in time to see what/where Watch #001 was, etc.
They, too, keep a log of severe weather events.....more fun!!!
Enjoy,