The HTML code will need to go into the HTML—which is presumably the layout editing. But don't just copy the whole lot. Just copy and paste the <ul> ... </ul> bit to start with, and perhaps the div around it.
At the bottom of the page, you'll need to include the <script> links ... but the link paths will have to change to the location of the actual scripts (which we still haven't determined you can actually place on this site).
The styles that go with that slider will have to go into the CSS area, but they will no doubt need to be modified.