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First: you've already taken a huge step by recognizing the problem. Some people are so bad at this stuff that they don't even recognize that they're bad at it. That's an almost hopeless position to be in. Especially people in the sciences often have a false sense of confidence about this stuff.


Second: it's damn hard and there's no easy route to getting better. You might get a CT textbook, but, honestly, most of them aren't very good/helpful.

I teach CT at the university level, and, though it's a freshman-level class, It's one of the hardest classes Iv'e ever taught. I've wasted way, way more time and energy trying to figure out how to do it well than I should have.

Honestly, I'd have a hard time giving manageable bits of advice, but here's a go at it:

[1] Get a copy of a collection of old LSATs and work through a few problems every day/week/whatever. Like this one:
https://www.amazon.com/10-Actual-Official-LSAT-PrepTests/dp/0986045519/ref=sr_1_2?ie=UTF8&qid=1483462117&sr=8-2&keywords=lsat

These are really good little problems. They're better than the exercises in most college-level CT texts. Yes, they're multiple-choice, and short, and a bit cartoonish in a certain respect...but they're very well-crafted, and you can check the answers.

It's the so-called logical reasoning problems that are really most helpful--i.e. not the reading comprehension problems or the analytic puzzles (ten monkeys sitting around a table; first monkey passes a block to the third monkey blah blah blah)--though those are also helpful.

[2] Find and follow some people who are good reasoners. I'm mostly sort of a centrist liberal, so my recommendations will be a bit skewed, but off the top of my head:
Kevin Drum at Mother Jones
Fareed Zacharia at CNN
Jonathan Chait at various places

[3] Most importantly, strive for honesty and fair-mindedness. Don't be dragged into the cesspool of rhetoric and debate. Just honestly ask yourself: what are some reasons for the thesis? what are some reasons against it? Are there any obvious problems with any of those reasons? Most people err in one of two ways: (a) they just aren't curious and don't care, or (b) they care...and so they end up getting committed to one side of the disagreement...and start consciously or unconsciously cheating.


[4] Also, PM me if you like, and I can send you some stuff and talk more about this stuff. I'm actually way better than average as a CT instructor...which means, IMO, that I still suck at it...but not as much as most.

There's no magic bullet--but you can get yourself on a trajectory toward improvement.

[p.s.: I kinda sorta disagree with chriswrightmusic, because I think that the fallacies are often of limited value, especially if not handled correctly...but I don't completely disagree with him.]

This book is also helpful to improve critical thinking skills: http://www.amazon.com/dp/B07MHQY9Q8

I cannot recommend Critical Thinking: Tools for Taking Charge of Your Professional and Personal Life enough.