Welcome to SQA.
Since you are new to testing I'd recommend you look at What does a Sofware QA Person Need to Know to Perform Their Job (Essentially)? for an overview of the things you should learn in order to be a good software tester. The field is HUGE and there's no way you'd be able to become an EXPERT anytime soon. Maybe 10-20 years down the road. lol.
The more you learn and understand about the basics of software testing the better you'll be able to understand how and when to automate. As Joe mentioned AST provides a number of cheap courses called BBST Foundations, Bug Advocacy and Test Design. The courses are intense but well worth it. The material is available for free here: http://testingeducation.org/BBST/ but there's so much to go through to understand things its best to take the classes.
Besides learning technical skills (languages, debugging, tools, etc.) you might want to learn When to Automate a Test. This is one of my favorite subjects of recent and Brian Marick has a good paper on the subject: http://www.uml.org.cn/test/pdf/automate.pdf
If you want to pick up technical skills I've found Codeacademy to be quite useful and so is Udacity in fact Udacity even has a course on Software Testing (although I haven't taken it so I can't say if its good / bad).