Did you contract an agency to build you a website, or is it one of these template things so common with hosting providers these days?
If the former, they will probably just send you the necesarry files when you ask for them. Depending on the website, you may be able to set this up yourself with your own host, or you may need to call in the help of someone, for what (unless it’s a very complex site) will probably be a fairly quick job. I use the term loosely though, because there’s no guarantees when it comes to technology and computers.
If the latter, you might be screwed, as you’re probably using their own proprietary software which cannot be transfered.
Will you be able to install it on WordPress? If it’s not already on WordPress, then no, it’s not that simple.