Is there a HTML technique for organizing my site's main pages in Google (navigation)? Or is it made by a Google's specific tool for creating a result layout like in this picture?

Look at the difference of the results for my site:

Is there a HTML technique for organizing my site's main pages in Google (navigation)? Or is it made by a Google's specific tool for creating a result layout like in this picture?

Look at the difference of the results for my site:

What you're talking about are Sitelinks. They're automated by Google so you can't really control them. You can, however, demote Sitelinks you don't link if they do start appearing.