What is the expectation that one should have from reading a published paper? Is it just to check that the paper's results are correct?  Should I expect that the authors describe their methods for arriving at the right answers / solving a problem?  I've often found that on a key part of the paper, e.g., the main result, the authors just give you the data without explaining.  I then have to verify that the data is correct and the results are correct but this takes a bit of work on my part, which I am happy to do, but I wonder why these steps aren't shown on the paper itself.

Is what I described the usual expectation when reading a research paper?  That I shouldn't expect researchers to divulge how they arrived at the right answer and perhaps that is a way for them to protect their work, e.g., whatever method they came up with that worked ... could have the potential to be used again and again to publish more papers?  

I also tried contacting researchers directly to discuss their work.  All of them are happy to talk - but mostly on a superficial level, e.g., "I've done X,Y, and Z, my co-author has done A,B and C."
I think there are two uses of the word "expectation" relevant to your question:

1) Expectation as in "standards": this would be the type of "expectations" a teacher might have of students: that they show up to class, complete assignments, read course materials, etc. This is the aspirational sense of the word.

2) Expectation as in "predictions of what is going to happen": a more realistic, perhaps Bayesian understanding of what publications are like in your field as you read more papers.

I don't think you are wrong to have high expectations in the first sense, especially from work published in high tier journals in your field. You should expect results to be presented clearly, empirical and statistical methodology to be detailed, and conclusions drawn to be clearly connected to the actual results and not just the predictions and world view of the authors.

In reality, your expectations in the second sense should not be as lofty. You should expect abstracts to not really tell you what limited scope the paper actually addresses You should expect to need to dig into not just the paper in hand but previous papers by the same authors and others they reference obliquely to figure out their methodology. You should expect to find conclusions that are suggested by but not shown convincingly by the data at hand. You should expect to find statistical approaches that are naive, inappropriate, or misleading.

In my personal experience, you will find authors in your field whose work you really cherish because they meet your Expectations. These won't necessarily be the most famous papers, but you will enjoy and learn from most of the publications they write. The other papers that instead conform to your expectations might be just as important, you will be held just as responsible to understand them and incorporate them into your work, but they won't be as fun, you will wonder how they ever got past peer review, and you might even start to doubt your field in general.

Don't fret! All you can really do is try to meet your own expectations.