The first thing you have to do when clicker training is to give the clicker meaning. Obviously, a simple click means absolutely nothing to the horse - and it may not mean anything to you. However, that can change for both of you if paired with something that IS meaningful.
The whole point of the clicker is to communicate "yes" to your horse when he does something correct (in traditional training, this "yes" is often a release of pressure). However, the horse won't know it means "yes" unless it's paired with something he wants. In most cases, horses will want food, so treats are often used with clicker training. It doesn't have to be treats, though - anything the horse will work for can be paired with the clicker to make it meaningful - maybe your horse likes a good rub on the neck? Treats are oftentimes the most convenient and motivating, though, and so from here on out I will describe clicker training like when it's used with treats (if you wanted to use something different and the horse does reliably work of it, just substitute your reward in place of when I say to give a treat).
So now, we have to teach the horse that a click means a treat is coming. There are two ways to do this. The first way is to "charge the clicker" - basically, you click and then treat, and then repeat. By doing this, the horse learns to pay attention to the clicker and learns that a click means that a treat will soon follow.
For me, I quickly lost attention and didn't really see any progress using this. Instead, I jumped to the next step to give the clicker meaning: targeting. Targeting is when the horse has to touch ("target") something. This is a very easy skill for the horse to learn, and, for me, it accomplishes teaching the horse that a click means a treat AND that he has to do something to earn it!
One principle of clicker training is that every behavior must be taught in baby steps. At first, the horse won't know what you want him to do. However, as soon as he does something in the general direction of your goal, he earns a click and treat. Sooner or later, the horse will figure out what it was he earned a click for and then do it over and over again. At this point, you ask for a little more before you click and treat (and repeat!), and eventually you've got the horse doing the behavior you set out to train in the first place.
So, back to targeting. I found the most interesting and odd thing that a horse would naturally want to investigate: A plastic water bottle covered in lime green duck tape. It looked funny, sounded funny, and smelled funny - perfect! I brought Flash into the round pen (you want somewhere small at first so they keep their attention on you) along with my bag of treats and clicker, then brought out the water bottle. I held it out with one hand a few inches in front of his nose. As soon as he reached forward to touch it, I clicked and treated. Of course, he didn't have any idea what had just happend and started looking everywhere for more treats - which earned him a firm smack on the nose. Pretty soon, he realized there weren't any free treats to be had, so he went back to investigating the odd-looking green object in my other hand. As soon as he touched it, I clicked and treated again! You could see the wheels turning in his head after two or three times, and within one session he was repeatedly nosing the water bottle and earning treats.
Now, Flash knew what the clicker was for - if he could play my game and figure out what I wanted, he could earn what he wanted. And it all was communicated through a simple click.