I would usually work with my horses every day to gain trust
If you have a round pen take them out into it and free lunge them then stop and turn your back to them, horses are naturally curious animals and if they feel safe the horse will come to you to see what you're doing
Grooming your horse is always a good way to bond with them and to show them you have good intent
Where you run around in circles and that with a lead rope on and treats then try taking it off and seeing if he follows you without the lead rope
Introduce them to anything that makes them nervous slowly and calmly. First let them see it from a distance, then let them see it up close. Let them smell it and let them approach it at their own pace. Soon they will realize that you won't introduce them to something that will hurt them.
I really think groundwork/lounging is the best way to gain trust and respect. Also, just spending time with your horse (grooming, grazing, etc) is also important when establishing a relationship. I don't really know how you can tell exactly...for me it's more of a feeling I have with my mare. Like when she listens on the ground or in the saddle, or when scared/spooked she looks for guidance and companionship, not shying or spooking.