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Earlier, Google used to display eight sitelinks - just links. But, now it's completely different. The recent update shows 12 sitelinks with a small snippet about your articles - not a snippet, probably the first phrase from your article. You may check out the screen shot below to better understand about the way in which the new sitelinks are displayed - sitelinks generated for "newbloggingtipz" on 19th August.
Since sitelinks are auto generated by Google with their special algorithms specifically written for the same, no one can actually tell you about getting sitelinks for your blog. However, I recommend you to read the following article which might probably fetch you one - How To Get Google Sitelinks For Your Blog? I also recommend you to install breadcrumbs for better results - Add Breadcrumb Navigation To Blogger.
Now, what if your unhappy with a link that appears below your domain name and you wish to remove the same. Very Simple! Login to your "Webmaster Tools" account and navigate to "Site Configuration>>Sitelinks" from your dashboard. Now, paste the URL you wish to remove and hit the "Demote" tab. That's it! Your done.
You'll not see that link from the next day - takes time to process your request. As such, you can demote upto 100 URLs and they are effective only for 90 days which means they might pop up again after a period of 90 days. So, you need to demote them every 90 days. You can read more about this topic here - Sitelinks.
Let me know if you made use of the demote/deletion tool to display better links to your readers? And do share your knowledge about Sitelinks with us via comments...