Hi,
I have forgotten this. But how to get this up as shown on the picture when looking at their domain name?
What is there to do to Google to find their domain and the content?
Tha magic word here is SEO, with different technics you can influence the way how search engine's handle your side.
I think it is related to SEO, mostly the pages with maximum traffic gets linked like that.
Like the two people said before me it is to do with SEO. You should build up backlinks but make sure they are unique and high quality articles, posts, replies.
SEO is one part of it, but also consider advertising on platforms such as Facebook and Twitter.
You can push the process a little bit by using google analytics service and google advertise service. But the effect is small... the most needed thing is seo and quality content.
A site without good content will never get attention from google.