How do I integrate CMS into existing site?

There are many people asking about how to integrate wordpress into an existing site, but pretty much all of them end up making their whole website run on wordpress. I ‘simply’ want to integrate it into my existing site page as a content management system, such as cutenews. I do not wish to run my site solely on wordpress.
If anyone could provide me with some simple steps to do this that would be great. I do not really understand the whole theme concept. If anyone has used cutenews, they will know what type of CMS I’m looking for. Only reason I’m trying to use wordpress is because cutenews has many security leaks.