How do .css files work?

Im taking a Web Development class, and we are learning html coding. We already made our first site in notepad. Already have the files saved properly also. Now we just learned about CSS files and that they are used to give the site a certain design. I know how to code them, but I dont know how to save them or where to place the code. Whenever, I click the index.html, the style isnt showing up. Can comeone breifly explain the basics of css and how to use them. Examples would be nice, thank you.