it most cases it can be estimated by calculations. See, for example, http://hyperphysics.phy-astr.gsu.edu/hbase/chemical/gibbspon.html
"Most common reactions can be assessed for spontaneity under standard conditions by looking up the associated thermodynamic quantities for each of the reactants and products. For non-standard conditions one can make use of the the expression for ΔG in terms of the other thermodynamic potentials..."
It also assumes that things happen at equillbrum or not very far from it. There are example problems worked here http://courses.washington.edu/bhrchem/c152/Lec08.pdf
However, I don't know if this is the "best prcess" for your particular situation.
To select reliable theoretical model for your reaction you should answer many questions:
Gas phase or liquid phase? Ground state, or excited states, homogeneous or heterogeneous bond scissions take place etc.
Please let us know more about your reactions. After could be try to select an satisfactory theoretical models, which they can give you acceptable Gibbs free Energy agreed well with experiment...
If it is in solvent phase there are many standard techniques, see below.
There are many implicit and explicit solvation models out there. In the explicit framework, you need to solvate (create a water box around your solute) your molecule in solvent (such as for water there are the 3point TIP3P, 4 point TIP4P, % point TIP5P, etc. ). Then you need to compute the solvation energy using standard thermodynamic integral techniques. You need to do this for your reactants and the product and then compute the difference for the energy of reaction.
In implicit models such as generalized Born or Poisson boltzmann it is sone using analytical tools. You can find reviews about these models if you google. AMBER/GROMACS etc. they provide both these techniques. Also there are more elegant and accurate and/or fast techniques developed recently such as RISM, Semi Explicit Assembly, Charge HydrationAsymmetric Generalized Born (this one is our work :-)) etc.
Gibbs free energy for a chemical reaction can be determined by temperature dependent study easily. By using Arrhenius and then Eyring equation we can determine change in Gibbs free energy as well as enthalpy and entropy.
It very much depends on which reaction you are talking about. For instance, in case of adsorption in an aqueous solution, one can do experiments at different concentrations of analyte to be adsorbed and at different reaction temperatures. Then by plotting Kd by 1/T (T in Kelvin) for a particular initial concentration of analyte, one is able to calculate thermodynamic constants - standard enthalpy of adsorption (ΔHo), and standard entropy of adsorption (ΔSo), based on a Van’t Hoff plot using the following formula:
Ln Kd = (ΔSo / R) - (ΔHo / RT).
ΔHo and ΔSo can be determined from the slope and intercept of the graph. Then ΔGo can be calculated from the following equation:
ΔGo = ΔHo - T*ΔSo.
Similarly one can calculate these thermodynamic constants at other initial concentrations of the analyte to be adsorbed
Check out my publications:
1. Zaynab Aly, Adrien Graulet, Nicholas Scales, Tracey Hanley, “Removal of aluminium from aqueous solutions using PAN-based adsorbents: characterisation, kinetics, equilibrium and thermodynamic studies, Journal of Environmental Science and Pollution Research (2014) 21: 3972-3986. DOI 10.1007/s11356-013-2305-6.
2. Z. Aly and V. Luca, “Uranium extraction from aqueous solution using dried and pyrolyzed tea and coffee wastes”, J. Radioanaly. Nucl. Chem., Volume 295, issue 2, (2013) pages 889-900. DOI: 10.1007/s10967-012-1851-6. Number of times cited = 4.
All my dears have given best options. I think the best way to determine the Gibbs free energy is that to determine the Cell potential by making appropriate arrangement for your substance.