Stories.
I've found that the signs are often very clear, but only after the fact.
My first cat started losing weight and peeing outside the box, for maybe a couple of weeks. Then I came home one day and she was really sick. I think her kidneys had failed. Took her to the after hours emergency vet, who confirmed she was really sick, and unless I thought she got into poison, that putting her down was a very humane choice. Came home without her, and felt like I really let her down (by not taking her in earlier), but it's probably unlikely the result would've been different.
Second cat, the Best Cat Ever was a better story. 16 very healthy years, then she started losing weight and mostly wanted to be on my lap, needing help to get up there, and I took her in when I saw this was progressing. Vet said there was really nothing to be done but it was up to me if I needed more time. She had given me so many good years I felt I owed it to her to not let her suffer, so I let her go that day. All I have is good memories.
Last one was throwing up a lot, very dark, which I learned was blood. I told the vet it was dark but must not have emphasized it and she missed it. Took her in a few times to try different things and she was getting worse. The stressor is that I had a week long ski trip coming up. The day before she had stopped eating, and was purring a lot. This was a rescue cat that I had never heard purr in 7 years, but I found out that cats also purr sometimes when they are sick, perhaps as a coping mechanism or to help with pain? I took her in, knowing it was probably the end. On the 30 minute drive I brushed her (her favorite thing) and told her stories about good times we had, and it kept both of us calm. The vet finally found a mass, and confirmed it on ultrasound, which she told me she didn't know how to read well so I guess that's why she never did before. Other than that, I really liked that vet. She said I could treat the cancer and perhaps give her another 6 months, but putting her down was a valid option. She knew my travel dilemma. I thought I'd feel guilty making that decision so I could go skiing but instead I felt a huge burden lifted as I was driving home, and only felt sadness.
I still had her litter mate, the new Best Cat Ever. I thought about leaving that vet, but decided not to. At last year's yearly checkup, she noted her losing weight, and suggested thyroid test, and that was low (or high? I forget now). I went with the radiation treatment and her weight came back up. I only did one thyroid follow up because this cat absolutely hates car travel, and I just couldn't see going through another cycle of treatment.
Sadly and shockingly, last month the vet was killed by a car as she was walking along a road late in the day. Guessing the driver was blinded by the sun and never saw her. I will switch over to a vet friend I met a few years ago. Only drawback is it's nearly an hour drive, with a cat that hates car travel.