Hi allWelcome to the world of Birds In Flight photography!
So my wife and I were walking in the park and she spots this hummingbird and points it to me. I have never seen one before, and got quite excited and worked up. The results were quite dismal (the best effort is below), so I am not even going to ask what I did wrong. But let's say this situation arises again, what should I do to ensure at least optimal results. I had a 135mm L attached to my 5dIII, ISO 160 (was set on Auto), f/8, 1/125 (was set on Av, forgot to change it in the haste). Thanks in advance.
From what I can see, you got a pretty good shot there. The only thing I might say is a little cropping might be in order (unless you've already done that to excess...) to make the Hummingbird more prominent.
Hummingbirds take patience to photograph, and even so, they move very quickly and seem to never be in the right place. I often photograph them at a local refuge, and I'll set up my tripod with a 100-400 lens (set at 400, usually) only 8-12 feet from the flowers they are attracted to. This is to nearly fill the frame with the tiny bird. And for every keeper, I'll have a dozen or several dozen where I got bird butt, half a bird, no bird, blurry bird, etc.
If you can crop it a bit, do that and frame it. It's a nice photograph!