Moreover, how is this possible with someone else’s website?
It’s not possible, unless maybe you’re a developer hired by the owner.
If you don’t own the site, you can’t edit it. It’s as simple as that. As has been said you can change how you see it, but you can’t change how anyone else sees it. That is totally different as you’re not really changing the site, but just changing how it looks in your browser.
If that’s all you want, find a browser extension that will let you override the site’s CSS styles.
Some sites will let you upload assets like an image or choose some options to customize your part of the site (like an avatar image, for example), but if the site doesn’t offer that option you’re out of luck.
If you want to add a background everyone can see, contact the site’s owner and see if that’s a feature they might add.