If you just acquired a new parrot – whether it is from a breeder, store, or rehomed – you will need to transfer it from the transportation enclosure to its new cage. The parrot may be in a travel carrier, crate, or cardboard box. Regardless, the procedure will be the same for getting it into the cage. There are several possibilities of how tame the parrot is. If you do not already know, you're about to find out. Bring the carrier into the same area as the cage. Close all doors and windows.
Most likely the parrot is quite scared so putting the carrier door up to the cage door will not be encouraging for the bird to come out on its own. Food lures won't work either since a scared bird will refuse to eat for several days. Your intervention will definitely be required.
You may be lucky and have a friendly parrot that already knows how to step up. The problem is that you may not know that in fact the parrot is friendly and aware of stepping up. The best way to test this is to open the carrier slowly and bring your hand toward the bird. As you open the carrier door, keep the opening minimal and blocked with your hand so that the parrot cannot rush out. Slowly bring your hand closer and closer to the parrot. If the parrot doesn't react to the hand much, then keep going closer. However, if the parrot is opening its beak and aggressively snapping toward your hand, then the stepping up method is unlikely to work.
For the non-aggressive parrot, keep bringing your hand closer and aim your fingers perpendicular to the feet. Depending on the size of the parrot you'll want to use anything from one finger to your entire arm. The main thing is to place your hand parallel to the perch it is standing on and slightly above its feet. If it was trained by the breeder to step up, it is a good idea to say “step up” as you have your hand positioned. As soon as the parrot steps up, slowly take it out of the carrier and then bring it into the cage. Like with your hand before, aim the bird in such a way that the cage perch runs parallel to your hand and slightly above its feet. The parrot should now step up onto the perch. You can close the cage door and talk to the parrot for a little while but then be sure to give it some time alone to adjust to its new home. I wouldn't suggest handling the parrot anymore at this time unless you are already experienced with parrots.
Getting parrot out of the carrier
If it turned out you are dealing with an aggressive parrot or it didn't step up using the method previously mentioned, you're going to have to get a hold of the bird to get it into the cage. Don't worry about this affecting your relationship. The parrot will eventually get over this. In fact it probably won't even realize what happened if you do it quickly enough. You definitely don't want to draw out this unpleasant experience any more than necessary as the fear will escalate and only make it more difficult to catch. It is especially important not to let the parrot escape the carrier if it is flighted because you will have a much tougher time getting a hold of it somewhere in the room.
Ideally you should just use your bare hand and grab the parrot out of the carrier. If you are too scared, you could wear thin leather gloves or use a towel. The best place to grab the parrot by is actually the neck, just below the head. Not only is it a safer place to avoid getting bit, it's also least likely to harm the parrot. If you grab by the belly, it could restrict airflow, but grabbing by the neck will not. By holding under the beak, you can keep the parrot from being able to turn its head and bite you. You can do the same with a glove. If you use a towel, you can either grab through the towel, or just get the bird in it and wrap it until you can get it in the cage. In one bold motion reach in toward the parrot. Even if it is backing away, just keep moving your hand toward it and back it into a corner. At this point the bird can't get anywhere and you can get a hold of it. Regardless of how you got a hold of it, don't prolong this and hurry up and get it in the cage. Whatever you do, don't let go of the bird (even if it bites). You'll have a much tougher time getting back if it gets loose in the room. If you had to use this more forceful method, it's a good idea to give the bird a bit more time to settle down before proceeding to taming and training.
If the parrot stepped up for you, the bird is probably quite tame and this basic taming should go much quicker. Since it is stepping up reliably, you will be able to ask the parrot to step up to come out of the cage. On the other hand if you had to grab the bird out of the carrier, odds are you will have to continue doing this until it has learned to step up.
No matter what method you had to use to get the new parrot into the cage, do not overwhelm it with attention immediately. Not only does it need some time to calm down and settle in, you also don't want to make it too dependent for attention. It is likely that the new parrot will eat little or none for the first few days. This should not be of too much concern. Just be sure that it has access to food and water and that it is already familiar with the food you are providing. This is not the time to try to do a food change or to instate any kind of food management for training.