For Clover, my dear cayuga, she stopped hanging around her friends as much, and started staring at walls. She stopped scanning the sky for predators, even though it had been her job to watch out for them. She just stood around and no longer engaged. When the rest of the ducks and I would take a walk Clover would stare at the barn 2 inches away from it and seem like she didn't know what was going on. She no longer came when I called and her personality was changed. This went on for about 2 days and I carried her around waiting to see if she might get better. Instead she stopped eating and I decided it was time. Since her disease was fatal I had decided not to keep her alive by tube feeding. On the way to the vet for her "goodbye procedure" she faded in and out of consciousness.
My other duck had severe aspergillosis. We treated for about a year before our vet decided it was fatal and I decided to stop the treatments. She had severe exercise intolerance and barely walk without gasping and wheezing. Once it was clear to me that she was in an unacceptable amount of discomfort, I took her in.
For me, I think some pain is ok. I have arthritis and migraine headaches so I understand pain and I don't want to be put down. But when one of my animals can't do things like eat, walk, or other normal activities because of pain, and there is no hope for them to recover, I feel like that is time to say goodbye. Of course, that is only my personal opinion for my own animals.
I always agonize over knowing when the time is right. But I always know. And I have never regretted my choice.