The Guardian made a great thing: everybody can take their content using Open Platform. You should register, generate a API key and, after that, on API Explorer generate content.
My question is: how to include content on my site? Where is the code? What should I do? I’m using Joomla to run the site.
If your site isn't running yet, I'd switch to wordpress. There is a wordpres plugin detailed on the guardian site which does exactly what you need.
There is no Joomla plugin available.
You will need to code one yourself - the Open Platform API returns XML or JSON response. If you don't know what that means, then you won't be able to code your own plugin, so I suggest switching to wordpress! Another alternative is if there is an existing plugin that will parse XML files for you?
Or you could just scrape content from the main site using my simple PHP web crawler tutorial published today - you'll need to wait for part 2 though! (And technically, it wont be entirely legal)