It really depends how the existing site is coded, as Dgold said.
WordPress is a really good platform for websites, not just blogs! Just by using the page feature, instead of post feature, you can create yourself a very efficient website! Content management systems can be FAR too complex for most websites (I know from experience!) and WordPress is easy to customise and add new functionality to... and did I mention the code is indeed poetry!
First though - coding. Is the site just flat html files with all the individual pages and content sitting on the server, or is it using a content management system (database driven content) like WordPress? Who hosts the website, and does your hosting plan meet the requirements for WordPress.
If your site only has a few pages, it would be best to copy and paste all the text out into a simple text editor (DONT use Word, it will probably copy lots of hidden formatting and screw up when you copy and paste it into WordPress in the future!!). Then save out the images for each page content - not the buttons and 'interface' graphics... that will come next!
WordPress uses a CSS based template system - if your current site uses CSS to control it's appearance, you should be able to re-use much of the old layout file, simply creating a WordPress theme using your old CSS (may be an opportunity for a spring clean!). A simple theme really can be just a very small handful of files
If you are lost at this point, I'd download a couple of themes and have a look at their files - some feature very complex code that do all sorts of clever stuff with option panels, and some are much simpler... the 'classic' theme that comes with WordPress is a simple theme and the 'default' theme is more complex.