eZ publish will automatically generate static parts of the content. E.g. the contents of an article will be stored in a .html file the first time it's requested. On the second request no processing is done for this.
The same applies for the content in pagelayout which is caced by the cache-block function. However some dynamic processing is always done by in the pagelayout.
There is different ways of doing a pure static site with eZ publish. There is one simple solution in our contributions archive: http://ez.no/developer/ez_publish_3/contributions/ez_sitecopier
This works great for many sites. You can choose which pages to generate static and POST pages will still work ( e.g. search/add comment ).
