[offlinedoctor]

I'm having trouble understanding how Henry's law applies to situations other than solubility,
I know the equation relates solubility to partial pressure, i.e. S = Kh (constant) X Pi (Partial Pressure), but I can't relate that to problems such as:

An atmosphere of pure methane at a pressure of 1.50 atm lies above a body of water. Assuming that
the system is at equilibrium at 298 K, what is the mole fraction of methane in the water?
Henry’s Law constant for methane at 298 K, kH = 4.13 x 102 atm.

By luck, these types of questions are either divide the two values or multiply, which appears to be the answer, but it's annoying me that I'm getting it right but I dont know why! 

[Borek]

Not sure what your problem is. You can calculate concentration of dissolved methane in water, then it becomes just a concentration conversion question.

[offlinedoctor]

Does the constant Kh have no relevance then?

[Borek]

It has. It has to be used to calculate concentration of the dissolved gas.