This is an excellent question, and one I hope others answer. Here's my personal take.
First, prune out really low quality sources of information, as they perpetuate uncritical thinking. The worst in my life are the Twitter trending tab (I did the "Indian Ocean" hack) and cable "news," especially the opinion section (and there's a lot more opinion stuff on even the "straight" news these days).
Second, spend some time editing Wikipedia articles, and become familiar with their guidelines. They are a digital community that has managed not to become a trash fire. My take is that being a decent WP editor requires a fairly low level of critical thinking - it can be defined as making good tertiary content (encyclopedia articles) from secondary sources, where the goal is simply verifiability rather than of truth. "Real" critical thinking might be defined as making good secondary content from primary sources. But I think the former is an important foundation. Did person X really say Y? If you get this wrong (which is super-common), there's no hope to answer deeper questions.
Generally, there is no "all in one" way of doing it. Generally active reading and checking the facts and primary sources will get you far. I don't think there is any substitute for reading lots and from diverse sources.
Four books that helped me along the way are:
How to Read a Book by Mortimer Adler
The Book of Fallacies by Jeremy Bentham
(alternatively, I enjoyed Logically Fallacious by Bo Bennet, and it fills the same niche)
First, prune out really low quality sources of information, as they perpetuate uncritical thinking. The worst in my life are the Twitter trending tab (I did the "Indian Ocean" hack) and cable "news," especially the opinion section (and there's a lot more opinion stuff on even the "straight" news these days).
Second, spend some time editing Wikipedia articles, and become familiar with their guidelines. They are a digital community that has managed not to become a trash fire. My take is that being a decent WP editor requires a fairly low level of critical thinking - it can be defined as making good tertiary content (encyclopedia articles) from secondary sources, where the goal is simply verifiability rather than of truth. "Real" critical thinking might be defined as making good secondary content from primary sources. But I think the former is an important foundation. Did person X really say Y? If you get this wrong (which is super-common), there's no hope to answer deeper questions.