My way of dealing with this through the foster dogs I had over the years was to let the dogs work things out themselves as much of the time as possible, within a strict set of rules that I had for myself. I never, ever left the dogs alone even for a minute, making sure one of them even came to the bathroom with me when I went. I've had things disintegrate in less than a minute when I am not in the room. They were always separated at night, using crates and/or baby gates.
I also monitored their interactions very closely, paying attention to the body language of both dogs. Any sign that things might get the least bit nasty, I distracted them and separated them. If the new dog was horning in on my dog's space, I would let my dog correct that without interference, but that was because I knew my dogs well and could tell if they were getting stressed, over excited, or giving warnings to the new dog. If my dog was getting stressed I would, same as above, distract and separate.
I made sure my own dog and the new dog each got separate time with me and time alone as well as time when they were both with me. And of course I immediately started with training the new dog unless that dog was traumatized and afraid. If the dog was able to be trained, I would start out with simple but important things like Wait, Come, Sit, the all-purpose "uh-uh" and Leave It as well as good leash manners.
A good relationship between the new dog and myself wherein the dog knew that doing what I asked would be nicely rewarded always helped a great deal in fostering good relations between the dogs, because it made it so much easier to distract the new dog or to break any tension that was arising.