I have two budgies, Peter and Sky

Keep loud noises down. Talk normally, so the bird isn't afraid of the silence. Birds get VERY paranoid when it's completely silent, because this normally means (in the wild) that some sort of predator is around. So play soft music, talk quietly amongst yourselves and keep an eye on the bird. Eventually he'll realize that he's not going to be eaten. He'll start examining his cage, maybe taking a bite of food or a sip of water. He'll explore his new little world and see that really, it's not that bad. It's actually kind of nice.

Once your parakeet has gotten over the initial fright, keep him reminded that you are a part of his new world. Don't run to the cage, don't make loud noises. But wander over and talk sweetly to him. Tell him he's a good bird, a pretty bird. Parakeets love words with 'hard' sounds in them like K and B and T. They learn those words very quickly. If your parakeet was hand raised, he may already be ready for finger-sitting, but if you got a bin-o-budgies bird, it may take a while. So spend the next two weeks focussing on this, because this is key. See Training your Bird to Sit on your Finger for help with that.

Once your bird is finger-trained, you can let him out to explore his new world! Make sure ALL doors are closed and it's even good to make a special sign to hang on each door saying DO NOT OPEN. You want to make sure it's extremely clear that a bird is loose so that the door stays shut. Birds love to fly! And now that your bird knows his home is the "safe place to return to" and also that your finger is the place to fly to, you can know that his explorations of the room will end with him returning home again.