When trying to solve a related rates problem, sometimes you need to relate variables. Can anyone help me with the conceptual reasoning or at least what to look for in these problems?
It depends upon the problem. Often such problems involve a particular geometric structure and then you look at things like the Pythagorean theorem, similar triangles, volume formulas, etc. Or if the problem involves motion, perhaps v= d/t.
It is a matter of looking for and recognizing relationships.
You pretty much always need to get a relationship (in the form of an equation) between the variables. The related rates part comes from differentiating both sides of the relationship equation to get a relationship involving the rates (derivatives).