As you would probably know, when your horse is happy and relaxed it gets a milky blue line around the eye, you can very slightly see it in this photo of Yorkies eye below.
When the horse is fearful the eyes go almost jet black.
Horse are unique in the way their brain functions, you would be familiar with the concept of horses stampeding.
Their brains function in such a way that when they are fearful they are unable to reason or think properly.

Hence when fearful and stampeding they run through fences etc, without thinking.
When their eyes are black they are fearful and unable to reason or concentrate or be safe for that matter!  We always need to keep our horses in the 'blue zone'  ie; in a state of mind that is relaxed and free from fear enough to reason and think.

The problem 99.9% of people make when a new horse arrives home is not understanding this simple fact about horse psychology.  A horse upon arrival will be fearful, will have black eyes, will be unable to think clearly or function reasonably or normally and is therefore unsafe.

The blue line in the eye is visible below in Yorkie's eye:

I learnt from a young age a relaxed horse is a safe horse, if you are in a hairy moment with your horse, one of the greatest tools in your arsenal for keeping safe on horseback is the ability to give it a pat.

A pat can turn black eyes into blue ringed eyes in a second.  Encouragement, gentleness, the ability to put your horse 'to sleep' while riding because it is so secure and relaxed is one thing every rider should learn.  It has been my one saving grace in so many hairy situations that would make grown men run and hide ;)

The eyes change instantly.  You can use this knowledge to know if your horse is relaxed and happy or not.

You will notice when your horse arrives and is in an unsettled state, it's eyes will be very black.

Your first step is to achieve a momentary blue ring in your horses eye.

It will need head space to process it's new environment, so needs to be put in it's new paddock immediately, do not lead it around, or attempt to brush or do anything with it, remember it is unable to think reasonably so will be in black eyed stampede mode.

Put it straight in the paddock and allow it the headspace it will need to grieve for the loss of it's friends and home and the total insecurity and fear that provides.

Also be aware the environment you place your horse into will also determine how quickly he feels secure.

They watch everything around them, as far as the eye can see, they study how gentle you are to other horses, people and animals around them, what goes on, and if there are any scary or intimidating things in the vicinity.  All these come into play. 

They are a herd animal, so ideally all horses should have other horses around.  If you can't and there are no other horses sometimes other animals suffice and if you can't, you just try to become their mate as much as possible while you are there.  Horses in  a herd take turns keeping watch and not sleeping overnight, if your horse is on it's own it will not be sleeping at night and will be cranky, unsettled and quite fearful.

Having a solo horse close to the house may help a little here.

But at some point, whether it be later that day or the next day, or when you can, try to achieve that blue ring, ie, treats and a pat, a pat and an encouraging word, etc... NO HALTER, NO FORCING THE HORSE TO BE WITH YOU, on it's turf, in it's paddock and on it's terms, when it walks away, respect this and don't force yourself on the horse.  You want your horse to feel completely free to come to you or to go away from you.  You are present but not as an authority figure but a friend only.  NO orders, no demands.

All horses are different and different things will work so you will get to know your horse and what he likes a little during this process.

This is the first step, the next step is not to be moved on to until you have achieved this blue line ;)

STEP 1  GOAL & OUTCOME: The goal & outcome of this step is for you to find a slight momentary effective and powerful connection with your new horse, and be able to find a way to make your horse momentarily relax and start to trust you.