Chickens that are happy will be active and scratching around in the grass, laying in the sun--yes, they do that, too!--or taking a bath in the dirt. We don't recommend YOU try that chicken behavior--for humans, water baths tend to work a little better. Chickens, however, use dust baths to help keep themselves free to parasites. They also may be looking for a good, private place to deposit their eggs. Happy chickens who go broody will try to sit on their eggs all day to hatch them, and will protest if you try to encourage them to leave.
If your chickens are ill, they will not be very active, and will often not leave the coop to do their usual things. Their feathers will be ruffled or puffed out, and their combs may be pale.
Chickens that are scared will try to hide or run away.
Some people think chickens don't get sad, but they do, especially if they don't have enough room to perform normal chicken behaviors like scratching and so forth, because their instincts are frustrated. This renders them helpless to do the things they need to! When they are sad, often let out very sad sounds that are unmistakable, the same way your dog might whimper if he is unhappy because he is hungry or needs to go outside.
When I lost my favorite hen to a predator, her sister cried sad sounds for several days, and looked for her in all her favorite spots. When she realized Lily was not coming back, she followed me around for days wanting lots of petting and attention. She was lonely! When my rooster was injured, I kept him inside to recover, and his favorite ladies would all wait right outside the sliding glass door to be as near him as possible. They missed him in their chicken-y way, and I had to carry them all into the coop every night after dark, because they wouldn't go in without him. Once he came back outside, they all went in every night on their own like clockwork, just as before.
If you watch your chickens closely, after a while you will be able to learn their body language and know when they are happy, sad, broody, ill, scared, mad or something different entirely.