How to Display summaries of recent posts in HTML

I’ve seen this before, so I think it’s possible, but is there a way that I can set up a script or somehting in an HTML file, like the index of my site, that will link to the most recent entry in my blog?

I’d also like to set it up so that a small excerpt from my recent entry in a specific topic could be displayed. For example, if I made a blog entry on something art related, i’d like to be able to have it automatically display the first paragraph of that entry in the html file where I have sketches and stuff displayed.

Again, i’m pretty sure there’s a way to do this, but my google-fu seems to be failing me. Any pointers would be much appreciated.