I think the most common way is to monitor the kinetics of your signal, either donor quenching (acceptor emission) in FRET or the change in helicity in CD. Then you can fit the kinetics traces to your model and see if the data agrees with your model.
Thanks. I am also trying to understand that how the enthalpy changes when the surrounding solution changes, for example what is the difference in enthalpy of two protein solutions, one in water and another in some other solvent.
Just about any physical technique that is sensitive to change of structure during folding can be used to address your problem. Those you mention are good, accessible and sensitive. If you are interested in kinetics, you must consider what time frame your folding occurs on. While most folding is over by a few seconds, some proteins require minutes or longer. Stopped-flow mixing will be needed to access the times of a few seconds or below (to milliseconds). Hand mixing (with stirring) can be used (without the need for specialized hardware) for reactions taking longer than a few seconds.
If you are only interested in confirming a 2-state model, you can simply record a spectra at equilbrium conditions under denaturing conditions and decreasing concentrations of denaturant. The presence of a isobestic point is a strong argument for a 2-state model. Note that the absence of a isobestic point does not however contradict a 2-state model.
For a two-state model you have to have just one single-exponential kinetic phase in both folding an d unfolding - consider the various time ranges Krut was mentioning! Stopped-flow plus "regular" kinetics (be careful not to bleach your chromophore during long kinetics!). Then compare the amplitudes on the kinetics with your transition curves - they should start at either native protein baseline signal or unfolded protein baseline signal and end at the respective equilibrium condition from both directions! For real two-state folders you should get the same results for both fluorescence and CD (and vis, and, and, and...). Transition curves that can bescribed by a two-state model are not sufficient as they 'only' indicate that there are no intermediates populated to such a degree that they can be seen in equilibrium. Sometimes, differeing slopes of the folding and unfolding branches of the chevron plot give a hint to different folding and unfolding pathways...
I agree with the answers of all previous very qualified researchers I only wish to remember that proteins are complex systems devoted to a biological function and sometime this activity is lost much before we can observe any significant CD variation in far UV region; relatively more sensitive to subtle changes of the tertiary structure are instead CD in the near UV region and fluorescence measurements....
@Daniele: yes, those spectroscopy measurements detect basically global changes and local changes that might dramatically affect activity, flexibility, proteolytic susceptibility etc. may be elusive...