Just out of curiousity..what it the correct way to build a website (software, etc)?
That is a very broad question but, fundamentally, you need your content marked up with semantically correct HTML (i.e. headers in h tags, paragraphs in p tags etc) and then styled from a CSS (cascading style sheet) that tells the browser how you want the HTML to be displayed. The key is to separate style from content.
The issue with exporting from Photoshop is that Photoshop doesn't understand semantics so you are not going to get a Google and user friendly website from that. People build websites, not computers.
As for software you can build a website using notepad if you want to.