Well, to fit any browser and not worry about CSS compatibility issues etc. then the <table width="100%" height="100%" ...> will ensure it behaves the same in all browsers. It'll stretch to fit the available width and height
It's not standards compliant and an all encompassing table has download issues (all elements must be read before any are shown), but it works.
You may have to use centering. You have to sit down and think about the different tables that make up the page. You have to imagine which table can be allowed to have 100% width. You will have one or more tables with fixed width. Like the table that contains the navigation.
What is allowed to stretch to 100% width is the main table where the content is. Then you'll see your text stretching and wrapping to fit the browser window.
Now the (somewhat) tricky part: The top portion of the page, where you will normally find a banner ad, or slogan, should have a component that is set to 100% width, so that it stretches out a COLORED or blank portion of the page, so that it looks cohesive (the opposite of falling apart).
To do all this well, you will have to use centering for some or all of the content/tables.