There are many ways to do it, but I have a similar set-up in which there is only one living space for all of my chickens. They have a coop, run, and access to partial free-range later in the day. When I add an adult, I treat them as if they are a new chick.
1.) Quarantine for approx. a month, if possible. In the past I've had trouble keeping a bird in total isolation for a whole month, which I say, is still pushing it if a month alone is not completed. This period is to make sure no one is ill, injured, or not feeling at their best. It can take a month to actually see something starting...I keep them in a dog crate inside my basement.
2.) After qarantine and all is clear, I take the bird, and can do one of two things, or both. I can put them in the crate out in the run and put a tarp over it, or put the crate in the coop, or both of them. I tend to keep them like this for at least a week. This way, they learn where home is, and who the other birds are from a safe environment. Although, a crate is small and birds get bored when there is nothing to do and can't go anywhere.
3.) Let 'em at it! Take the bird out and see how they interact with the flock. There should be squabble, because a new pecking order must be decided. If there is bloodshed, take the injured bird away and treat them before throwing them back in the flock again. Sometimes it takes more than one try, and even more than JUST ONE DAY to have everything work out. Be patient. I usually put the bird back in the crate and try again the next day, and the next, and so after. I don't like to leave them at the mercy of the flock after just one day.
People say that when a chicken wakes up the next day with a new chicken there, they don't notice and there is less fighting. In my limited experience, this is very untrue. Chickens are not too bright, but they aren't oblivious to the scenes around them, especially because they are territorial in their own home. I find that they do notice new things and there is more fighting when they first meet, and have the ability to bloody themselves up.
A tip: In the past, when I've added young chicks, I put some big, colorful children's toys (trucks, bikes, etc), and maybe a potted plant or two in their run when I added the new birds. As said before, chickens notice change in their own home and they are more interested with investigating eye-catching items than they are with newcomers.