I haven't had to look into this lately, thank goodness, but years ago I was told the most humane way was either the overdose of clove oil (which acts as an anesthetic), or affecting anesthesia with clove oil and then freezing.
So I was curious and did a little research on more recent recommendations. Here is the article I found to be most logical and trust worthy:
Aquarius Aquaria - Exploring Fish Euthanasia
If I were to chose a method now, I would go with placing the animal in alcohol (as pure as I could find, perhaps Everclear or 90% isopropyl alcohol
available at my work). I would be very careful not to cause undue stress in capture.
Unfortunately, I'm all too familiar with euthanasia because of my job. I applaud anyone who shows animals respect and compassion up to and including the end. Here's hoping for long healthy fish lives!