Design without tables is how I do the majority of my sites. Are they more SEO friendly…. That’s debateable. Many say yes, but search engines certainly can read tables just fine.
As far as ‘How exactly do you design a site without tables?’
Basically, you use DIV tags and a lot of ID’s / Classes with CSS. All the formatting of the site is in the CSS. This not only allows your page to be ‘clean’, but allows you to quickly change the layout / look / color scheme of your site.
Hope that helps.. It’s getting late and my mind is a bit fried. 