What I've noticed about "critical thinking" is that it's a skill most adults have been using in one capacity or another for some time. What throws people is putting putting a name to it. For some reason, it freaks people out. Equally strange is the way instructors approach the idea. They seem to treat it like it is a totally new concept that's not to be experienced outside of nursing. (Ok, ok... there ARE people for whom this is a totally new concept.. but that's a subject for a different thread...)
Basically, all that's being asked is that you look beyond the obvious first impressions. For example: If you are a parent, you've undoubtedly found that certain situations are indicators that something is not/potentially isn't right. "Hmmm. It's been too quiet for the last 10 minutes." A non-critical thinking approach would just stop at the "quiet" part and figure all is well. The experienced parent will realize that the quiet is often assocaiated with your kid getting into something that they really shouldn't be messing with (or worse, have come to some harm that prevents them from making any noise). So based on your experience, you've put together a set of conclusions and/or possibilities that may be at play. Based on those conclusions, you then take action, collect more data, etc.
So the skill shouldn't be all that foreign to you. The "new" part is that you'll be pulling from what you're learning in nursing-specific course work. What you're being asked to do is to make the mental connections between the patho, pharm, psych, etc. etc.
As for testing, my experience has been that the test that you get in your typical college exam doesn't require anything more than simple recall from rote learning - decidedly uncritical thinking. (Of course, that's totally contingent upon the skill of your instructor, quality of the institution, etc.) So getting study guides for NCLEX are helpful in exposing you to the sort of questions that you're likely to encounter. Most of these guides also include the rationale in how the answer was arrived at. Do the question, run through the rationale in your own mind, and then compare it to the rationale that the test developer used. Then... do a truck-load of those questions to get used to thinking of questions in the terms you are likely to see on the test.
It's not easy. But neither is it impossible.