The buzz word you are looking for is Sitelinks (link to the explaination), well google does not tell how you can get these site links, but taking a shot in dark at the algorithm it seems that you need to build your website with a very good navigation system, meaning the navigation should be in proper <nav> <ul> <li>
tags, have proper title. You should take care of the sitemap both (sitemap.xml and html sitemap), micro-formats, structured data etc.
One more thing to note is that Google shows sitelinks only for search results that rank at the top, so it is most important to have your website rank at top position for some keyword.
I reckon you follow all the SEO guidelines by Google and you should have the sitelinks, it is not really difficult to get.