Make sure the horse is comfortable drinking your water and hay. Some horses may not drink or eat if they are uncomfortable.
Avoid riding the horse right away, spend time with it to see how it acts, the reactions to certian things, etc.
If the horse is spooking when you try to tack it up then try to rub the tack your using all over the horse. This tells the horse that what your doing is not going to hurt it and neither will you.
Even if you get it from a safe place, get the vet to check out the horse immediatly, in case something when wrong in shipping or the horse did something to itself while traveling.
One sign of a healthy horse is if it has diareah in the beginning. This means that the horse is uncertian about the new place but it knows it will be okay.
I hope I helped :)