I like to start with grooming. Grooming is a great way to get to know a horse and to build trust. Why? Because if you open up all your senses, be present in the moment, turn off your cell phone, not talk to your buddy, and truly focus on the horse, s/he will tell you volumes of information about him/her self.
The horse will tell you where on his body he is ticklish, where he is in pain, where he likes to be scratched, where he is comfortable being touched and most important where he is NOT comfortable being touched.
When you have all of this valuable information, you can use it to gain the horse's trust. You may still be asking, well how do I do that?
First off, nothing with horses is every truly quick. It takes time and consistency to build a quality relationship with a horse. However, I have found that grooming will allow you to build trust with a horse in about a week - as long as you listen to what the horse is telling you and you are consistent.
Here's how you get started. Honor the horse and not touch him where he doesn't want to be touched. Only touch him where he is comfortable. The key is to BE CONSISTENT. You don't gain a horse's trust overnight!
As time progresses, the horse becomes more relaxed with you. You begin to see his comfort zone expand, and then you are able to touch him very slowly in areas you where you were not able to touch him before.
Always read your horse's body language and feel/sense if s/he is comfortable with what you're doing.
If you listen to your horse in the beginning, honor his untouchable zones and progress at his pace, this is how you build his trust over time. Each horse is going to progress at his/her own pace based on his/her previous experience with humans. Remember that slow is fast when it comes to working with horses.