How do I know if I am styling the Mobile Website or the Desktop Site?

Along with what Alexander said, you can also check how the site looks on different screen sizes by opening Chrome developers tools, and then opening the "Toggle Device mode", it's a simulator which lets you see your website on different devices. It's pretty handy.

You start with the mobile. Make the site look good on small screen resolutions like on a phone. Later you will learn about a media query which will allow you to make changes to how your site looks if your site is viewed on larger resolutions like a tablet or desktop. If your site is viewed within a specific resolution size, the code you write in the media query will run and adjust the look of your site. It's just easier to start with smaller resolutions as they are generally less complicated. The main layout of your site will look the same but you can make it look better as the screen that your viewer is using gets larger. In short, the desktop site adds css to the mobile site as the screen resolution increases