By proper calibration you get the Cp(T) curve which provides the entropy term (integral of Cp/T dT) see

http://www.engr.ucsb.edu/~shell/che110a/heatcapacitycalculations.pdf

If additionally you have first order transition, you will see an enothermal peak, which gives you the enthalpy term and  G = H -TS is the free enthalpy

Actually the second description is much more detailed and technical than mine :)

Agree with above discussions. First, you need to calibrate your system with a standard sample. Ideally the calibration should be done with the same heating rate and gas flowing conditions, using mass comparable to the sample to be measured. Then, you determine the entropy of your sample by comparing the respective areas of the peaks.

Everything is correct, but entropy of a compound at T is given by integration of

dS=Cp/T dT  from 0 to T. This determination require a low temperature (often adiabatic) calorimeter, starting at liquid helium temperature or lower.

Of course, here "heat capacity" Cp is dH/dT , and not the partial derivate of enthalpy, which is the correct definition of heat capacity. Hence enthalpy is given by integration from 0 to T of dH/dT     

Thanks for your answers.

The free energy of the glass transition actually cannot be calculated from DSC because glass is a nonergodic and nonequilibrium material and the equations presented assume equilibrium temperatures. This is something I came across recently in research and was surprised to find a wonderful paper from Mauro et. al in the Journal of Chemical Physics discussing this issue. The DOI for the article is given below:

Article Heat Capacity, Enthalpy Fluctuations, and Configurational En...

Article Response to 'Comment on 'Heat capacity, enthalpy fluctuation...

Article Continuously Broken Ergodicity

Hope this helps