Q:

Move a website over to CMS

I have a static website that has been built by converting psd to xhtml/css and includes a little PHP.  This is the extent to which I design websites at the current time.  
My client has now informed me on whether it would be a difficult process to incorporate a CMS into the website.  Now I know what a CMS is and I know the common opensource systems like Drupal, Wordpress and Joomla. 
My first question is :-

Would I be incorporating one of these CMS's into my website or the website into a CMS? 

and

Is it a long process to get a CMS integrated? 

A:

Would I be incorporating one of these CMS's into my website or the website into a CMS? 

That wholly depends on how you and your client want to manage the website.  If the client only wants to be able to "blog" then it's easier to add the CMS to your website for specific pages that the client wants to manage. 
On the other hand, if the client wants to manage the entire site via CMS, then you would be building your site in the CMS of your choosing. 

Is it a long process to get a CMS integrated? 

It depends on your familiarity with CMS's.  I can speak on wordpress, as it's the one I'm most familiar with--once you've built/selected/customized a theme that matches your original website (or the look for your new site), adding content is fairly easy.  In my opinion, the biggest time spent is in customizing the theme. 
Edit to add:
If time was the consideration, my approach would be to either buy a theme online that the client agrees to, or subcontract out the Wordpress theme design to someone who has a lot of experience building custom themes.  The latter option is not "cheap" by anymeans, but there are a number of freelance designers who do design wordpress themes. 