Chickens do get sick at some point in their lives. But you can avoid many issues by keeping your birds wormed on a regular basis. Round worms are everywhere and are devastating killers if they are not kept at bay.
Keep your facilities as clean as possible. Cleanliness is the key to good health in many ways.
Use proper ventilation in your coop. Approximately 1 square foot of vent space per bird in the coop. Chickens put out a lot of moisture through pooping and breathing. This moisture needs to go somewhere. It tends to rise and if your vents are put in properly, this moisture will go up and out the eaves. Slanted roofs are nice because the air enters on the low side and goes out the high side. Have the chickens roost lower to the ground out of this moving air. They will make their own heat bubble and all moisture is wicked away. Poor ventilation causes all kinds of respiratory issues and makes for lots of frost bite as well when the water falls back down as frost.
Don't over crowd your birds. 5 square feet per bird in the coop, 10 square feet per bird in the run. This helps with aggression and over all health.
Make sure you have enough food and water stations. Higher birds in the flock can starve out the lower ranking birds which can lead to dehydration and egg binding, or starvation and weak birds. So at least 2 stations for a small flock.
Feed them right. Keep the treats down to 10% of the diet. Hens need large amounts of nutrients to lay eggs and will draw from their bodies if they don't get it in their diet. This leads to weakness.
Probiotics....can't say enough. 70% of the immune system lies in the intestinal tract. Harmful pathogens tend to take hold here and they don't stand a chance in an oxygen rich healthy environment.
Get them out to free range! Good for exercise and burns calories, breaks up boredom and stimulates their minds. Less chances they will turn aggressive on each other when they get outside time.
I am a crop checker. I check them every morning and each night at roosting time. A healthy bird will go to bed with a full crop and will awake with an empty one. If either of these isn't as it should, something is wrong.
So just a few ideas. Unfortunately birds do get sick. But you can prevent many issues along the way. Get to know your birds. Sit with them and know how each of them works. This way you can spot if Lucy is off one day. Or Ethel looks like she isn't all there today. The sooner you find something wrong and treat it, the better the chances you can save them.
Oh and always buy chicks or grown birds from places you trust like hatcheries or private breeders. Swap meets, Craigslist and other unknown sources can sell you sick birds.
Good luck! :-)