Lets start by explaining what Google sitelinks actually are and what they look like, a number of popular websites have sitelinks, the vast majority do not.
If you search for "pebble web design" you will see we have sitelinks, this is because (we are not getting big headed here) google sees us as a website that has not only useful information but wants to help the user find the most useful information more quickly on our website.
You can clearly see the visual benefits of having sitelinks as the user is drawn to the options available and more than likely, one of the options is going to be something you are actually looking for.
From a website designer/developer point of view, the only way you can get yourself down the route of even starting to get Google to think about awarding your website sitelinks is to make sure you have a clear navigation structure, clear logic to links on your website, do not have links more than than three clicks away from your root pages and have load of useful information that people want to read.
If and when you do get sitelinks you can manage these from your Google Webmaster Tools account, including removing any sitelinks you do not want displaying.
Resources Available:
Google Webmaster Tools