The video below features an excellent description of this scientific "attitude" from famed skeptic Michael Shermer. He describes science as a "Baloney Detection Kit," and describes some general rules for thinking scientifically.
Some things to watch for:
- His descriptive of our tendency to see patterns, especially illusory correlations
- His specific mention of confirmation bias as a source of error
- In point #3: the need for replication of research results
- In point #9: a description of the nature of scientific theories...and how they are different from what most of us casually refer to as "theories"
My personal favorite quote: "You want a mind open enough to accept radical new ideas, but not so open that your brains fall out."