Hi,
There are likely to be a number of factors that play a part in this, although there is no rules from Google on how to achieve it. If there were, people would be changing them based on what they want, rather than what Google wants. It is also worth remembering that Google only show these for brand searches, so a strong brand is important.
That said, if I were looking at this myself, I would include the following:
- Clean internal linking structure with good anchor text
- Correctly code your links to ensure they can be fully spidered
- Links to your desired pages
- Pages with a low bounce rate and good organic traffic that already appear in the SERPs for their desired phrase(s)
- Unique page content that is no duplicated anywhere else
- Unique and appropriate page titles and descriptions
There is never any guarantee that you can influence these sitelinks or have Google guarantee a demotion, but follow a bit of best practice, and you might have some success.
-Andy