Jeanne, is correct. You should only need to add the MySQL driver when you try to run your application. My mistake.
I am completely new to Eclipse, so bare with me.
I believe on the main tool bar, there is a "Run" option. From there if you choose "Run..." and then choose the run as "Java Application" configuration, then click the "New" button, At that point your program name(Test3) should appear and also it should bring up a tabbed menu. At that point you should see a "CLASSPATH" tabbed menu option. From there you should be able to browse your filesystem and add the MySQL driver to your Application.
Like I said I am new to Eclipse there may be alternative ways of doing this.