After tinkering around with LinkedIn for a bit it was exceptionally confusing to understand how to actually get your blog posts to show up on your user profile like below. This blog post explains how to do it in a step-by-step fashion with any type of blog.

Basically, the TypePad sponsored BlogLink application for LinkedIn looks at each website you provide in your user profile and looks for an RSS or an ATOM feed on that page. If you are using WordPress or TypePad the BlogLink recognizes it automatically. For HTML and content management driven sites it takes a bit more work.
Step 1
Click on the RSS icon at the top of your blog website:

Step 2
This will then take you to the RSS feed version of your blog. This basically renders a page using predefined XML tags that RSS/ATOM viewers can understand.

Step 3
Copy and paste the URL in your address bar here into the blog link on your LinkedIn profile by going to http://www.linkedin.com/myprofile?editAdditionalInfo=&locale=en_US&goback=%2Eprf_en*4US.
Step 4
Install the BlogLink application by going to: http://www.linkedin.com/opensocialInstallation/preview?_ch_panel_id=1&_applicationId=1500.
Conclusion
All around this application was a great addition to LinkedIn. I think that LinkedIn or TypePad could have provided a bit of documentation before installing the application or possibly a configuration section on the application. But now, you know how to do it anyways!