When I go out to my coop, these are the things I look for which indicate a problem or sickness:
Chicken by itself, fluffed up, head pulled in, eyes closed, moving slow or not at all, not eating or drinking
Chicken not walking easily. You learn what "normal" chicken behavior and movement looks like, by just watching the flock when they are free ranging or just in their yard, then you can very easily spot abnormal movement or walking
Listen for coughing, sneezing, wheezing - good time to listen is in the evening after they've settled down to roost
A chicken that doesn't leave the hen house to go out into the yard, even when treats are being given out
Missing feathers or bald patches on back, head, tail, rump
Discharge from eyes, nose, mouth
Breathing with mouth open
These are some of the things that I watch for on an everyday basis. If I see a chicken doing any of these things, I bring her inside and do a more through examination. The ease with which I can catch her tells some things too.
Depending on symptoms and the course of treatment I pursue, I usually put her in my isolation cage in my house for several days. That way I can very closely moniter what she eats and drinks. This also allows me to give her medicine in her drinking water without having to medicate the whole flock. And by having her in the house, I pay close attention to her general behavior and improving or worsening condition.
Hope this helps.
Sarah