You will want to edit your main.tpl file in include/template/main.tpl use the information here

under website intergration, which tells you roughly how things work
http://punbb.informer.com/docs/dev.html#integration

and then read about importing php code into your main.tpl template here under 3.4, which is how you are going to call your headers and footers and sidebars around the forum.
http://punbb.informer.com/docs/faq.html#faq3_4

And if you want a real world example then this tutorial is very handy, even though it uses wordpress as a cms it will explain all the finer points of pulling through headers and footers around the punbb forums.  Showing you where you want to be copying stuff across
http://www.liewcf.com/blog/archives/2005/04/integrate-punbb-forum-into-wordpress/

and also this one
http://almosteffortless.com/2005/09/25/integrating-wordpress-and-punbb/

Hope that helps or it should at least get you started, tried to keep it short:)

I am looking for clues on how to integrate punBB within fundanemt CMS (fundanemt.org).
I'd like to implement it on this page: http://www.ebenalp.ch
My idea is to add just the forum-output of punBB without doc type, header, footer etc.
I don't want to add markup from my existing site to punBB's template, but rather want to render punBB inside a CMS-generated page.

Any pointers would be greatly appreciated.

Cheers,
cmyk