Do you have pictures of your chicken coop and run? How large is it?
Most people will use the "see-no-touch-method". Chickens are territorial and can seriously injure each other, so the goal is to introduce them safely over a period of time.
When I attempted to integrate, I used a 4x4-foot doggie playpen with hardware cloth cable-tied along the bottom foot (so no one could reach in and injure the chicks). This allowed lots of face-to-face interaction between the two groups. I also encouraged them to eat close together and offered treats for positive association.
Once the birds start to lose interest and ignore each other (which can take a few days), I'll test the waters. There needs to be lots of space, lots of clutter, and multiple feed/water stations. The pecking order will come into play, and the newcomers will be smacked and chased a bit. They need to be able to escape (hence the clutter to run behind). I do monitor during this time. I don't want to see any sort of relentless pursuit or full-blown fighting. If that happens, we go back to the playpen separation and try again once things settle down.
It can be a slow going. I've seen people just throw birds together and have it work out. I've also seen gruesome injuries from rushed integration. My chickens are my pets, so I play it conservatively.
I'm sure you'll hear from others with more details, but I hope this helps give a general idea of the process.
It is definitely doable but it has to be done correctly.
