Often life curves are given in alternating pseudo-stress, which is total strain multiplied by the modulus of elasticity. It is not real stress because when the material exceeds the proportional limit, the relationship between stress and strain is no longer linear (hence, sigma ~= E*epsilon).
In general, to use these plots, you would compute the stress with linear-elastic assumptions (beam theory, linear-elastic FEM, etc.) and then use the results to determine the minimum life of the component being analyzed.
Note that in most FEM analyses of metals and the like, you'll report your results in a bulk stress (Von Mises, Tresca, etc.). If using a von Mises stress; you'll need to determine the sign of the maximum and minimum values. A signed von Mises stress is often determined by taking the sign of the largest of the principal stresses (in magnitude) and applying it to the VM stress that the model outputs.
You need to be sure to use a stress-strain curve with the correct stress ratio, as that has a significant affect on the life of the material. If you don't have a curve with your exact stress ratio you can either interpolate between curves (if you have at least two) or do a Walker transformation.
I find the biggest challenge in any fatigue analysis is finding credible material data. Mind the temperature of the part that your analyzing and compare that to the temperature at which the curve was generated. Higher temperatures tend to reduce fatigue life (unless you're talking about really very cold things that experience a ductile-to-brittle transition).
A good general reference for fatigue analysis is the Atlas of Fatigue curves. I'd recommend giving it a once-over.
