Minification and Compression Basics

I’m totally new to web stuff, and have recently learned about minifying CSS, javascript and HTML. how does this occur? do i run it on my files manually in a dev environment and then publish them to the live server?

what about gzipping? i’d like to hear about what a good workflow would be for optimizing a wordpress site.

I’ve been using google page speed tool and the results it gives me mean nothing ??

any tips or links to good resources would be appreciated.