What is the most drupally way to add a slide show (as a block? So I can reuse it in multiple places)
If the content you want to use is already in nodes then you could use Views and Views Slideshow (which uses the cylce plugin you linked to).

With views you can create a block which can be re-used wherever you want in the site.

Learning how to use Views is one of the best things a new user to Drupal can do, it'll provides a lot of nice tools in a point and click interface.