Bringing a new bird home is exciting. You have (hopefully) done your homework and are fully prepared for the new addition but if you already have other birds, please take these precautions.
You want to quarantine the new bird to avoid introducing disease to your other birds. Always start with a vet check and have the bird tested for communicable diseases. Never introduce a new bird to your flock without a proper quarantine period. It’s recommended that you keep the new bird separated for a minimum of 30 days, but 90 would be better since some illnesses don’t show any symptoms until after 30 days.
Keep your new bird as far from your other bird as possible, preferably in a different area and a separate ventilation system. At minimum it should be a separate room with the door closed. During this time you need to be very cautious about sanitation. Wash your hands after caring for the new bird. Have a set of dishes and toys that are ONLY used for that bird. Don’t use quarantine dishes for the others in your flock. Clean cages daily starting with your existing birds and moving to the new bird.
Once the quarantine period is over, introductions can begin. Start off by placing the cages side-by-side for a few days or even weeks and see how it goes. If you have a neutral space that isn't already dominated by the bird you currently have, that would be a great place to introduce them. If you don’t have a neutral zone then the next step would be to place the cages apart enough so they are near one another but not close enough that they can walk onto the other’s cage. This becomes a little tricky if one or both are flighted so make sure you keep a close eye on things. Open the cage doors and let them observe each other. Don't have any expectations because not all birds will get along with others, but there is a good chance they will.
As far as a neutral space, at the rescue I have a few Java trees set up that are not in the main rescue room. This is a quieter, neutral space that has actually worked really well to help birds assimilate into the flock. I have many birds that come into the rescue that have been an "only bird" and the prior owners were concerned whether the birds would do well here with so many other birds. We have had some great experiences where birds are interested in the others and end up flying from tree-to-tree to get to know one another, much like what would happen in the wild. There have been a few times where there was a little aggression so of course we separate, give it more time, and try again later.
The biggest thing to remember is to go slow. Keep a favorite treat on hand and praise when they get along but be ready to coax them away if they don’t hit it off at first. Just because they are birds, even if they’re the same species, that doesn’t guarantee they will like each other. They can be and should be taught to coexist and respect the other’s space and will certainly benefit from the community environment.