How to add extra css in style.css file?
Yes, if style.css is a CSS file that's loaded into your page (either by a module or, more likely, your theme) then that's probably a good place for your custom styles.

If you'd rather have your own file for custom styles though, you can just create a file (e.g. custom.css) in your theme folder, and add a line like this to the theme's .info file:

stylesheets[all][] = custom.css


Once you clear Drupal's caches you should see the new stylesheet included in all pages using that theme.