use Google webmaster tools. if your site appears on top for a keyword for a long enough time, you will get sitelinks
i have find around 20 keywords phrases that my site appear in first and second place of the results with the option see more results from bidlink.eu but i havent find the magic keyphrases yet....Also this 5 months they change from 6 to 3 from 2 to 8 sitelinks and different urls for sitelinks so maybe thi is the reason why they not appear,maybe because they are not stable...For the OP wait usualy take 2-4 months before the appear in searches if they just appear on WMT.
Well my diabetes Corner blog has many Site Links. Search this term without qoutes in googfle and you may know site:diabetescorner.blogspot.com 295 links in google link:diabetescorner.blogspot.com 1 link only
Now this was really funny like your image. It's sitelinks not the backlinks you see using link: operator.
Sitelinks frustrate me.... for my site Google is putting links in that it just shouldn't be. I keep removing them in Webmaster tools so eventually it will slot in the right ones. It would be nice if webmasters could recommend links to use.