It is as straight forward as it looks. You need to have data on the anisotropy for various film thicknesses, t. Make a plot K_eff vs 1/t. Obviously you should get a line with the slope being the surface anisotropy. There is plenty of literature showing how to do this. Search for example for Ulrich Gradmann. He has a review on magnetic surface anisotropies.
An alternative approach to determine surface anisotropy constant K_s is measuring spin wave resonance spectra. K_s enters surface boundary conditions and influence on the resonance frequencies (fields).