One of the primary ADVANTAGES of CSS is that (if properly constructed) the site will degrade gracefully for older browsers.
Actually, the biggest compatibility problem with CSS is with browsers that A LITTLE old. i.e. those that support CSS, but support an older version than you are using. You may need to provide multiple style sheets for different browsers.
Alternately, you can provide NO style sheet for older browsers that don't support your version of CSS, if you can not justify the time and expense of creating alternate stylesheets.
For a really old browser, though, that doesn't support CSS at all, insuring compatibility is a matter making sure your text appears in the correct order (don't put the last paragraph first and then reposition it with CSS!), and few other simple rules, along with checking in an old browser (or with CSS rendering turned off) to make sure that it makes sense.