Clearly the pulse should be checked when your cat is relaxed and at rest. You can measure the pulse with two fingers of a hand. Place the ball of the fingers (the area of the finger that is the last joint of the finger, on the side opposite to the nail) just inside the thigh of the cat. This will allow you to sense the femoral artery, which is near the surface in that area.
Alternatively, if your cat is slim enough, (mine isn't) you can feel the heart itself by placing your fingers over the area of the heart behind the left elbow. If you simply put your hand on the cat's chest you can feel it sometimes and then home in for a more accurate reading. If you time the pulse for 15 seconds and multiply by 4 that will give you the beats per minute. If the pulse is weak this may apparently indicate anemia (I am not a vet). If over 200 beats per minute this may indicate a heart problem or an overactive thyroid gland. See the veterinarian.
Photo: in public domain.