The links shown below some of Google’s search results, called sitelinks, are meant to help users navigate your site. Our systems analyze the link structure of your site to find shortcuts that will save users time and allow them to quickly find the information they’re looking for.
1: The main search result
We only show sitelinks for results when we think they’ll be useful to the user. If the structure of your site doesn’t allow our algorithms to find good sitelinks, or we don’t think that the sitelinks for your site are relevant for the user’s query, we won’t show them.
At the moment, sitelinks are automated. We’re always working to improve our sitelinks algorithms, and we may incorporate webmaster input in the future. There are best practices you can follow, however, to improve the quality of your sitelinks. For example, for your site’s internal links, make sure you use anchor text and
alt text that’s informative, compact, and avoids repetition.
After some discussion & analysis, we’ve decided to remove the “Demote Sitelinks” setting in Search Console.
Sitelinks are the links shown below search results on some queries, to help users navigate your website. Over the years, our algorithms have gotten much better at finding, creating, and showing relevant sitelinks, and so we feel it’s time to simplify things.
We only show sitelinks for results when we think they’ll be useful to the user. If the structure of your site doesn’t allow our algorithms to find good sitelinks, or we don’t think that the sitelinks for your site are relevant for the user’s query, we won’t show them. This process is completely automated. Sitelinks have evolved into being based on traditional web ranking, so the way to influence them is the same as other web pages.
Best practices to improve the quality of your sitelinks include:
# Provide a clear structure for your website, using relevant internal links and anchor text that’s informative, compact, and avoids repetition.
# Allow Google to crawl and index important pages within your site. Use Fetch and Render  to check that they can be rendered properly.
# If you need to remove a page from search completely, use a “noindex” robots meta tag  on that page.
Should you run across undesired sitelinks for your site with common queries, feel free to drop by the webmaster help forums  to get advice from other webmasters, and to let us know about it. We appreciate all feedback on our search results, and use it to help further improve our algorithms over time!
 Fetch & render: https://support.google.com/webmasters/answer/6066468
 Noindex: https://support.google.com/webmasters/answer/93710
 Webmaster forum: https://support.google.com/webmasters/go/community
You can determine the information displayed in search results by entering title and description meta tags for each page.
To improve the chances of getting sitelinks:
- Organize navigation so that it presents a smaller number of options, based on what your visitors choose most.
- Brand your site with a unique name so that your site doesn’t get “lost in the crowd”.
- Make sure your meta tags are accurate.
- Add useful outbound links so that even if your site was not exactly what visitors were looking for, they do not return to their initial search results.
here is some old info, but it is useful info