1. Log out from Drupal (or use another browser) to browse around your site as the anonymous user. Ensure that static files are indeed being generated into the Boost cache directory; and if you opt to use gzip, likewise check gzipped files are being generated in the directory you specified for this. The ( Administer > Performance > Boost settings ) page shows how many pages are cached by Boost.
2. Check the Drupal status page ( Administer > Reports > Status report ) for any errors or notices.
3. To check whether you have a cached or dynamic version of a page, look at the very end of the page's HTML source. You have the cached version if the last line looks like this:
<--Page cached by Boost @ 2009-08-11 06:19:58,expires @ 2009-08-11 09:19:58-->