Commenting on blog posts works by reblogging the original post into one's own blog and adding a comment. Comments are visible to subscribers of the commenter's blog.
The reblogged post would be wrapped in a new message that would be posted to the reposter's blog. The new message would include a signature by the reposter and an optional comment, and it would be distributed to the reposter's subscribers in the same way as a normal post.
Reading a few Tumblr blogs is the easiest way to understand how this style of commenting works. See http://awkwardvagina.com/ for example (don't worry about the URL, it's just a typical Tumblr blog full of reblogged memes and jokes).