I hear a lot about "clicker training" but don't really know what it is...whatever it is, does it work?
OK, I will try not to bore you too much with this (speaking on this subject used to be part of my job, and I could literally give a 20-minute lecture on this subject. No one wants that! I already talk too much as it is.). But, I am no expert. I have been familiar with the principals of it for quite some time, but have only just actually started using it. There is probably someone on here much more qualified to speak on this than me!
Here is a very thumbnail version of the history/principles. Clicker traning is a form of training that uses positive reinforcement - basically rewarding the good stuff and ignoring the bad. It was originally developed by dolphin trainers (mainly Karen Pryor) for working with animals that were not easy to train using "normal' methods.
You teach the animal to associate the sound of the click with something good, usually food. You click and treat, click and treat, until the animal knows that the click sound means something good is coming. Essentially, the click sound says to the animal "Yes! You did a good job". It becomes a way to tell them that they are doing the right thing. If I ask Ranger to sit, and he does, I click and treat and he knows that sitting was the behavior I wanted. If he offers a sit without being asked, and I click and treat, he thinks "Oh, ok, she likes it when I sit down. Good things happen when I sit". Eventually, over time the click may even come to be rewarding in and of itself.
The other thing the click can do is act as a bridging signal - way to bridge the amount of time between the animal performing the correct behavior and the animal getting rewarded for it. It specifys the exact instance in time that the correct thing was done, and can help you "shape" a behavior. Let's say Ranger walks over to me, puts his paw on my knee and then lays down. I tell him he is good and give him a treat. What was good? What did he just get that cookie for? Was it coming to me? Pawing me? Laying down? How does he know? Now imagine that same sequence of behaviors, but this time I click when he lays down. He knows that out of all those things he just did, laying down was the one I liked.
BTW, it doesn't even necessarily have to be a click. Dolphin trainers often use a whistle. You can even use a word, like "good". Most trainers prefer the click, or other non-human sound, because it is consistent and sounds the same way every time you make the sound. The human voice carries a lot of tones and inflections, and therefore can be inconsistent to doggy ears.
So, that is my lecture. Hope it wasn't too boring! I recommend giving it a try. You will probably need to so some background reading to get started, but eventually you would probably be able to shape the behavior of your dog staying by your side, or at least coming when called!