There are many techniques. Z-scan is the most widely employed and is simple in design. Look up Sheik-Bahae and Eric Van Stryland's paper in Quantum Electron, it is the definitive paper on the subject. Others also use FWM and third harmonic generation. You'll need to know the structure of your sample to use the nonlinear index and absorption coefficient to calculate chi 3 properly. Many nonlinear optics text describe which matrix elements are the same for which types of crystals. If you are looking for chi2, second harmonic generation works, you will just need to know something about the phase matching angle.