The approach behind solving a structure elucidation problem is very similar to attempting a math problem or working on a jigsaw puzzle. This similar mental framework shares a basis, but not limited to, on understanding the basic rules that define the problem, and in some cases the creativity and flexibility to redefine the problem.
When presented with a set of data, an elucidator can recognize that the data is valid and logical, address any problematic areas and explore a strategy to fix or solve it without making too many assumptions. Although various problem solving techniques exist, ultimately, it is experience that goes a long way.
The following reference addresses some of the underlying issues described in this blog: J.E. Davidson and R.J. Sternberg. The Psychology of Problem Solving. Cambridge University Press, 2003.