I've been fostering for rescues for 20 years and have fostered over 1000 dogs during this time. It's not too bad to integrate a dog into your pack, but it takes thought and consistency. If you throw them together and don't cut off bad behavior, you may get two dogs that fight constantly. First, assume you are going to be crating the new dog for most of the day for the first 3 weeks, in the family room, where you are most. It's important they see each other consistently, but not be able to fight. Then when you take them outside to go potty, you take both for a good fast paced walk. Two people are needed. Each walks their dog and keeps the dog focused on the walk, not the other dog. No greetings, just walking, 4-8 times/day. After a week or two, if the current dog seems relaxed, take them to a neutral place that is fenced. If you're worried about a fight, get a Marine Air Horn from Amazon to safely break up a fight. In the neutral place, leave the leashes on, but drop them and back off. If either dog tries to put their neck over the other, IMMEDIATELY say a LOUD "AAATTT" and simultaneously cut it off to distract. One dog putting their neck over another is a prelude to a fight, within seconds. If one dog is intently sniffing the ground or yawns, that is good, if the other dog doesn't continue to overwhelm the 1st dog. Those are diffusing & calming signals in dog language. If neither dog is possessive of toys, we try to keep the dogs active together, while insuring no dog is overwhelmed. We do this for a week or so, gradually increasing the length of time they are together. Then try walking dogs and doing the same in your outside back yard, and finally allowing them for short times together, supervised in the house. The goal is to never have a fight because once you have a fight it's much harder to integrate them.
It's VERY VERY important that when you work with the dogs, you feel calm and happy. If you're stressed and nervous, it can cause a fight. Dogs react to the moods of the people. The walking helps both people and dogs to get rid of nervous energy. My attitude is always somewhat like my kids...you're going to behave and get along. If one is too hyper, tell them to knock it off. If they won't wind down, they go to their crate. Once and awhile, I can know two personalities won't be good and we pair the foster with a different play group.
Hope this helps...