This depends on if you’re talking of your blog’s front/home page or if you’re talking about feeds, like the WordPress Reader.
For displaying a shortened extract on your blog’s own home page, you can insert the “more” tag into a post at the point where you want it to cut off. You’ll find the icon in the toolbar of the post editor. It looks like a dotted line between two thick lines. You can only use it once per post. You can also break a post up over several pages using the nextpage tag. Instructions at http://en.support.wordpress.com/splitting-content/nextpage/
For showing an extract on feeds rather than the full post, go to Settings > Reading from your dashboard. The fourth heading “For each article in a feed show” and then you can select either full text or summary.