How do you find the constant of proportionality?

The short answer: through experimentation and measurement. Long answer: let's regard that we have a block with some mass on a level surface that is attached to a spring. The relevant equation is F = -kx. The spring constant, k, gives a measure of the spring stiffness and varies for each different spring. By setting up this scenario, one can attach a mass to a spring that is attached to a wall. You can stretch out the mass and spring system by some distance x (in meters) and measure the force that is necessary to do so. Plotting the distance on the x-axis and the force required on the y-axis, you will find a linear graph. The gradient of that simple, straight line will be the spring constant.