Create a template without tables from a table-based template for a GENERIC website

My website is centered around a generic set of PHP scripts and HTML templates. It is GENERIC and NOT a WordPress site. Although the scripts perform excellent, the HTML template is poorly designed with tables nested inside other tables. To speed up display of the site, I need to port the current table-based templates to one without tables. Although the template contains 20 files, all of these files are basically composed of two tables, i.e., one in the header and one in center of the pages. This project is, consequently, about re-formatting two tables into two based formats. I need to mention again that this site is NOT a WordPress-based site but generic.