I do not see any "share" buttons to generate public link. Please show on the screenshot.

Sorry, the button has moved since the screenshots in the blog post were taken.

You can find the Share controls in the right hand side panel on the activity detail page, see http://blog.gpsloglabs.com/post_images/activity-panel-share.png

Once you click that, hopefully the rest is self explanatory, but the following blog posts contain more details if you need them: http://blog.gpsloglabs.com/tag/sharing.html