Doctors Lau and Chan from the University of Hong Kong have made a wonderful site to teach you critical thinking, logic, scientific reasoning, and other such skills.
That page is a good resource and offers good tools and methods. Critical thinking, logic and reasoning have a place in all aspects of life, whether they be work, home, hobbies, studying, or something else.
For example, such skills are especially useful today as media exists all around us (radio, TV, Internet, iPad, newspapers, magazines, ...) and bombards us constantly with different information. Often this information is presented not by a neutral messenger, but by someone with an agenda. For example, this someone may want to alter your opinion, or to sell you something, or to confuse the issue. Spotting the agenda allows you, for example, to make an informed judgement about the quality of the presented information, to consider whether it is something to be ignored altogether, to find out the actual meaning behind the message, and so on.
If you want some media-related training material after studying the Critical Thinking pages, I suggest this:
- pick up three different newspapers or websites for the same day
- find an article about the same piece of news
- observe how it's presented differently (hopefully it is): what is missing, what is emphasized, what words are used and what words are not used
- consider: why is it presented differently
Note: There is no right and wrong answer to this exercise, the point is to use your newly-acquired skills.
Another example of usage areas would be to use Mill's methods (explained on the site) for analyzing and understanding software engineering problems, or to find out why your used car might be behaving strangely, or what is wrong in the electric installation in your house, etc.
There are simply a great number of ways how and where these fundamental and powerful skills can be used.