This is, unfortunately, something I was never exposed to as an undergraduate or in my PhD core (economics).
As an example, suppose I'm looking at three well-known nationally representative surveys: recent estimates from the American Communities Survey (ACS), the General Social Survey (GSS), and the NLSY79. Suppose each has an aggregate variable I'd like to use in an analysis of income, and further suppose each of the three independent variables are unique to their respective surveys.
I suppose cross-sectional analysis is out, since I'm dealing with different respondents. It also seems like doing a time-series analysis would be tricky if the surveys were administered at different times (the examples are).
In short, what can I do, if anything, to observe interesting patterns in the data? What's kosher, and what's faux pas with regard to using results from different surveys?