Essentially a landing page is a static page (basic page) on your website where you would target one location and one service type and add a call to action (an instruction on what you want the visitor to do, i.e. call you, email you and so on.
In a nut shell that is what a landing page is. It isn't rocket science as some people may lead you to believe!
So for your website to rank for the areas you want to work in, you would have many landing pages on your website.