Here's a simple article that shows how to easily plot the BH curve of and inductor.
The basic lashup goes a little something like this: stick a sampling resistor in the primary, run the secondary through an RC integrator, feed both into an oscilloscope that can do XY plotting, drive the primary from a Variac, turn the knob, and watch at the results. You might want a bit more finesse than this, but, eh, it works.
The primary voltage will be relatively low, so plug a 12 VAC wall wart into the Variac. This gives you galvanic isolation from the power line, finer control over the primary voltage (more of a full turn on the Variac), and will prevent you from killing yourself or burning out your basement laboratory. You want a fairly husky wart if you’re measuring husky inductors. Remember: this is an AC measurement, so you want an AC wall wart, not one with a nice filtered DC output.
The resistance of the sampling resistor should be much less than the inductive reactance of the coil. We’ll measure it at 60 Hz because that’s easy, so for a coil of inductance L, the reactance at 60 Hz is 2 * pi * 60 * L. That simplifies to 377 * L, so a 1 mH coil has about 400 m-ohm reactance. I have a nearly infinite stash of 100 m-ohm sandbox power resistors, so that’s what we’ll use; you’d want less, but this is quick & easy.
If the inductor doesn’t have a secondary, poke some magnet wire through the core. Use some simple number of turns and remember that number, just in case you want to calibrate the results.
The time constant of the RC integrator must be a lot bigger than the frequency you’re integrating. For a 60 Hz signal, you want maybe a 6 Hz integrator: 60 Hz -> 17 ms, so pick 200 ms. Having a nice 1 uF film cap in my heap, the resistor works out to (200×10^-3) / (1×10^-6) = 200 k. Anything in that range will work fine. A larger cap gives you a smaller resistor and more signal to the scope.
http://softsolder.com/2008/12/28/inductor-saturation/