How do I save a wordpress theme’s files and install them on another site?

If your theme was developed correctly all of your assets should be stored in:

/wp-content/themes/theme-name/

Simply copy your theme folder and drop it into the same location on a new site. From there you can activate it via Appearence -> Themes in your WordPress backend.

If you have any plugins you need to copy over you can do the exact same thing with plugin folders too. You’ll find those at this location:

/wp-content/plugins/plugin-name/