A cat’s vital signs are (a) temperature (b) heart rate and (c) breathing rate.
The temperature can be checked with a digital ear canal thermometer. See picture. Supremely easy or relatively easy! Target: 37.8° – 39.4°C.
For heart rate: use your smartphone’s stopwatch! Feel your cat’s heart beat by placing your hand “over his left side, just behind his front leg”. Time the beat for 15 seconds and multiply by 4. It should be 140-220.
For breathing rate: You observe the movement of your cat’s abdomen and chest when he is relaxed and standing. The number of movements over 60 secs is counted. It should be 20-30 breaths per minute.
See also: The signs of a healthy cat.
My thanks to VCA Animal Hospitals: Check Your Cat's Vital Signs at Home | VCA Animal Hospitals.