I don't own a goat (sadly), but I know how people use clickers for dogs.
The first thing you would want to do would be to "load the clicker". You probably know this step, but for anyone who doesn't...To do this, you will click the clicker, then give the goat a treat. This process teaches the goat that the click means food is coming. Do this until you can tell the goat is starting to make a connection. When you click, the goat may perk up, or look to see if food is coming, that's how you'll know you've loaded the clicker.
Clickers are only used to mark a behavior. I don't use them because I prefer saying "yes", which works just as well, at least it does for my dogs. Whatever method you choose is up to you and your animal.
Anyways, step two: train your goat!
I'm not sure which tricks your planning on teaching your goat, but if it's something the goat does naturally, wait till the goat does it, then click and give the goat a treat. With enough repetition, the goat should learn that food comes when he does a certain behavior.
Good luck with your goat! I hope you'll keep us updated on how the training goes.