I have a html website – if I wanted to use a CMS how hard would it be to change my website?

It’s not at all hard, however it is a question of time depending on the complexity of the existing website and what the CMS-based website will include feature-wise. So it is entirely possible to convert a ‘static’ (aka unchanging) website to a CMS-based platform like WordPress or Joomla. I once converted a 12-page static website to WordPress* within two weeks, including a content-refresh and image optimisation to make the website faster to load.
In most cases, the design of a static website is likely to be old and tired, and this raises the opportunity to completely re-design your website. In a lot of cases doing a re-design by using existing WordPress themes will be quicker and cheaper than trying to convert the static site like-for-like into a CMS,
*I am a WordPress expert and therefore naturally recommend WordPress as the website CMS of choice.