s-l-o-w-l-y
There are a lot of variables, but one thing to recall is that chicken-time moves at a different pace than human-time, IMO. So drag the process out for as long as you can. If you have particularly calm breeds, and if the chickens are used to each other, you and they will have an easier time of it.
1. They should be able to see each other for long enough that they are all familiar with each other by sight before integration. (They should mostly ignore each other).
2. If you can free-range them together for a period of time, they can begin to work out their new pecking-order with plenty of space and room to run if someone is getting picked on.
3. Make sure that there is lots of feed and water (extra feeders and waterers if you can arrange it) when you put them together.
4. Some people slip the chickens in together at night so they will all wake up together in the morning. Make sure that it isn't just one new chicken (if you can) being put in with older chickens.
I just put my 2 BPRs in with my new Ideal 236 and Easter Egger, but they have known about each other for about 4-months now. There was no great drama, and now they are all living together, but there is still a little pecking going on when one of the younger ones irritates one of the older ones. One thing mine started doing was visiting the coop of the other ones when all were free-ranging. One evening, I just closed them all up in the larger coop----and since then, they have been sharing space together. I do also let them out of the coop and run to free-range in the morning and most of the days that I can arrange to be around.
Hope that you get lots of good replies for this question, and good luck with your combination.