Tepid,
I developed critical appraisal skills as I was required to appraise scientific literature, that was a ramp to my critical thinking. If you google 'develop critical appraisal' it will provide many resources on how to do this.
I think you have asked a great question, but a hard one to answer. It may be that there is a gap in the market exactly for this. In an information age that arrived acutely, many of us were not are skilled to sift through the information and be usefully skeptical.
For me it is about evidence. The better the evidence the more reliable the idea is PROBABLY. The less evidence the less time or interest it has from me. Some people confuse skeptisism and critical thinking with being close minded, it is quite the opposite. Sure question EVERYTHING, but promoting mysticisim because it is close minded to reject the supernatural is not focusing on......evidence.
I wish I could give you a better answer, if I think of one I will come back to you. I must add that watching hundreds of intellectual debates will help you see how others are figuring out their way through life, it isn't the data in these debates that I found useful but approaches to the data, the thought process.
Before long you see where honesty and truth (very scientific) becomes hope and comfort (believers) as people sit on a spectrum of reliance on evidence.
The it is about deciding where you sit on the spectrum.
It is an exciting, protective and interesting journey , if not tiring, to figure everything out for yourself, enjoy it x