Please read the first Thread in the Amazon Forum: Amazon Body Language. Better said, set you chair along side your Amazon's cage or perch and read it aloud to him. And, repeat this a couple times a week. In fact, anything you are reading, including this Forum, read it aloud to your Amazon. This in and of itself will go along way to reducing his nervousness i.e.: the comfort of your voice!
Good things always happen when you and other family members are around! Get everyone involved that is in the home. Everyone has a stake in this and therefore everyone needs to be involved. Everyone needs a job that brings something important to your Amazon. Water, food, toys, cleaning, etc... Point being, your Amazon is the center of his new family.
Target getting him out of the cage ASAP. Whether that is step-up to a finger or a hand held perch. You will need to avoid cage dominance.
Avian Vet Visit: This should also be ASAP.
There has been tons of diet information in the Amazon Forum. Point being, a solid, balanced healthy natural diet support with a solid healthy dry diet is a primary requirement, the sooner the better. No Sun Flower Seeds!
Cage: Lots of toys, especially hanging toys that by placement will create a safe spot for your Amazon to retreat too. Set a large diameter natural perch in an upper corner and set the hanging toys around it. If you do not have a Cage, see the Cage Forum. In general, the larger the better. Target a full height door - the first time you will need to clean that cage, you will love that door! FYI: Hanging toys work on the outside of the cage also!
Although you will not likely enjoy the instant bonding that can and may happen to some. I can assure you that if you fully commit to this process, the Love and Joy that you commit will come back to you at levels you will not believe.
NOTE: Your Amazon will likely be more comfortable on perches commonly sized for MAC's. Target natural perches at 2.5" diameter and larger. Complete a Web Search for Handicapped parrots (or birds) and target foot problems. There is great information available.
Expectations: Expect near nothing and rewards for near anything! Overload the Love. If you start from nothing, everything is up! And, that is a wonderful thing for everyone! Your Amazon wants to be part of your family and wants to be some place safe and loving.
Its Never The Amazon's Fault! Its always your fault. Work from this view point and you will quickly solve problems and move forward.
Keep coming back: Amazons and the people they own are a wonderful group, after all "Amazons Rule!"
PS: As BIRDMAN state, slow and steady, so move a little slower on getting him out of the cage!