I just looked at your site and it seems that currently the first few posts have "Continue Reading" link. So maybe you already figured this out.
I believe you're referring to the setting for RSS feed, which is on the Settings -> Reading page: "For each article in a feed, show". This will not effect how post are displayed on the site though.
You can use the More Tag in the editor to set custom "Read More" on your posts. Here is good overview on how to do that: http://en.support.wordpress.com/splitting-content/more-tag/
Also, depending on which theme you're using you can sometimes use the Excerpt field on a Posts: http://en.support.wordpress.com/splitting-content/excerpts/