How do get my sitelinks to appear on Google search results?

You can get sitelinks in Google's search results, but takes time. Suppose if you want to get your product page under site links, you need to promote it and see that you get lot of hits to it, the page should be user and search engine friendly. It should appears on top pages with your target keywords. Now its up to you how you promote it online, once you get good hits to the page with top ranking you can get the results in couple of months.
What ever I suggest above as per my experience, you can try but I can't guarantee it'll work.