Put the outputs of them to an emission shader and experiment on a few objects while rotating the scene. But in general…
Fresnel (node): For dielectric materials like plastic, wood, and glass (not metals), it allows you to control the reflectivity so that it is more reflective at grazing normals than normals facing you. If you use it to blend between a refraction shader and a glossy shader, you should get the same results as when using a glass shader, and it’s done by entering the correct IOR value for the medium you want to simulate. Or rather, the ratio between two materials - if camera is in water looking into a glass object, glass should have a different IOR compared to when camera is in air/vacuum. Metals are pretty much fully reflective all around, and doesn’t require fresnel control of glossyness (enough to matter). Blender currently doesn’t support more complex aspects of fresnel equations, like handing polarized light or complex numbers required for metals (but again, just ignore fresnel for metals). The IOR (Index Of Refraction) approach is nice if you want to simulate things accurately, or need to recalculate new IORs based on one of the mediums not being air/vacuum. You can set IOR to like 8-20 for metals, but the effect will be hardly noticeable. But these values may “feel strange” to handle, so…
Fresnel (Layer Weight mode): This is the same as above, except you don’t give it an accurate IOR number, but instead some value between 0-1 which may “feel easier” to handle mathematically speaking in a node tree. I don’t know how the numbers correlate, so I guess this is just a matter of eyeballing it until it looks about right. I don’t think I have ever had a “need” to control IOR in this fashion (like, varying it across a material), but I sometimes use it to observe differences in output and usability (by experimenting) for the facing approach (next).
Facing (Layer Weight mode): This varies output linearly based on if normal is grazing or facing you. This, unlike fresnel based, is very intuitive to use in nodes since its output is consistent between 0-1, and although specular control is not its intended use originally, it has become a popular way to achieve better and more intuitive controls for PBR (physically based rendering, which is an “ease of use” paradigm more than a “physically correct” one). If you do newangle=oldangle^4, and make sure it doesn’t go below 4%, you’re basically covered for all dielectric (non metals) materials (minus probably gemstones). It’s a very rough approximation, but it produce consistent and easily tweaked results.
Two reasons why fresnel might be avoided as a rule of thumb:
- It’s output isn’t always in the 0-1 range, making the output hard to handle further down the node tree.
- Fresnel for any kind of transparency requires a solid, it will not work (as intuitively expected) at all for flat planes.