How do I get sitelinks to appear in my site’s search results?

The first thing I had to figure out when asking this question was, what the heck do you actually call the links that appear under the main URL when searching for a brand or a publisher?
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How do I get sitelinks to appear in my site’s search results?

The first thing I had to figure out when asking this question was, what the heck do you actually call the links that appear under the main URL when searching for a brand or a publisher?
More