Quarantine Program is the first thing you will need to do before your introduce any new birds to your existing birds (flock).
Here is a method that I have used and found to be useful when introducing a new bird to the existing flock. This method is primary to be used if you are introducing in a small setting (such a inside cage or a small aviary). Those who have large aviaries may have different methods since the situation is different.
When I introduce Pretty to Merlin it was a gradual process. When quarantine was over these are the steps I took.
1. I first let them out together on top of the cage with complete supervision
2. I kept their cages side by side but not where they could beak fight or pick at each others toes. So about 2 inches apart
3. I then let Merlin go in Pretty's cage during the day supervised only
4. I then let Merlin go in Pretty's cage during the day unsupervised only after I knew that everyone body was settled.
5. After I knew the daytime unsupervised time was OK, I then housed them together.
Now not everyone may do what I did but this is why I did this.
When I first introduced them Pretty thought Merlin was a girl (he was a boy) and kept trying to jump on his back plus he was very hyper flirting like mad. Merlin kept refusing his actions of love :D and would do a lot of dolphin noises.
I moved on to the next step when Merlin was doing so much dolphin "mad" like budgie noises and Pretty settled down.
For me it took just a little under 2 weeks. Everyone is different some members can put their budgies in straight away (after quarantine is over) but I could not.