Adding New Chickens to the Flock

Before adding new chickens to your flock, make sure they are healthy. And if you have adult hens make sure the new chickens are at least 4 months old before introducing them so they are all about the same size. To be safe, I made the introduction process spread out for a couple weeks. Before I got the new chickens, I made a temporary cage next to (or inside) the coop so my chickens and the new chickens can see each other during the day but not have physical contact. Make sure they also have food and water, and if laying, a nesting box. And even a small perch for them to roost on if you want, and shelter from weather and predators. 

After picking up the new chickens, put them in their temporary cage and give them plenty of water, food, and treats to be occupied during the day. Keep a close eye on them because the new chickens, since being separated from their flock, may be re-establishing their pecking order and may fight a bit. I've found that it's easiest introducing chickens that are younger than my flock because they are more likely to be submissive and will get the pecking order established sooner with less fights. Especially introducing a rooster that is younger and smaller than the hens is best so then he won't beat up the hens as much since they will most likely be dominant over him for a little while. I've also found that introducing hens to a flock with an existing rooster is harder because he views them as intruders, whereas hens seem to accept new comers faster.
After a couple weeks of getting used to each  other, I let the new chickens out of their cage during the afternoon. I've found that lots of space is key for introducing the new chickens. This way everyone can be more distracted and less likely to fight so much. I kept a close eye on them all day. If one of the chickens is wounded or being really naughty, then you may have to separate her/him for a little while to cool off or heal.
By the end of the day, the new chickens should be going into the coop at night with the others. If not, then just put them in until they get it. I have a coop with a run attached to it that the chickens can freely go in and out of. Some of my new chickens would just roost outside in the run at night instead of the coop. If it's warm I wouldn't worry about it. But after a few days they were still not going inside the coop, so I would just put them inside the coop, on a lower perch away from my flock, and soon they got the idea.
Another good thing to remember is that every 2-3 hens added, I added another nesting box. And every 8-10 chickens added, I would add another food and water feeder so that everyone will get a chance to eat at the same time. Also the more chickens added, the more roaming space will be required to prevent hen pecking.