There are a few different ways to put a Cmap into a blog post. If I wanted to be lame, I could make the map into an image either by taking a screen shot or exporting the map as an image file, and then insert that into a post. The reason I call that lame is because the map loses its links.
You can make Cmaps into web pages directly from the program menu: File – Export Cmap As – Web Page. This generates a JPG image of the map and an HTML file. To get that HTML into a blog post, it has to be online somewhere. I use the online storage service Dropbox, and upload the HTML and JPG to the Public folder.