“Test automation shouldn’t be a goal; test automation helps you achieve goals” -Jonathan Kohl. Read More Here
Many think that,the place to start learning the art of Automation is the tool one uses.But with my experience I would say that the place to start is OOPS.Then understand the basics of technology in which the application is developed. For example,If you are automating a web based application,then be familiar with HTML,DCOM,COM,DHTML.
Get some working knowledge on SQL, Connecting to DB through the automation tool,XML,FSO (to interact with files) and COM objects of MS Excel(read and write data to excel sheet),MS Outlook(to e-mail reports)
Then get to know the coding language or script tool uses,then understand how the tool recognize your application, get to know the available functions.
Now your are ready to automate your application,now decide on the Automation Framework ,come up with Automation test plan and Estimations(separate article coming soon )
Read this link on more details about getting started with automation.
Addendum Added on Oct 2.2009 : Please read Testing Vs Checking by Michael Bolton before jumping into automation