This answer adds to the solutions above to address your last sentence that reads:
how do I ensure that sub-left and sub-right stay within sub-title
The problem is that as the content of sub-left or sub-right expands they will extend below sub-title. This behaviour is designed into CSS but does cause problems for most of us. The easiest solution is to have a div that is styled with the CSS Clear declaration.
To do this include a CSS statement to define a closing div (can be Clear Left or RIght rather than both, depending on what Float declarations have been used:
#sub_close {clear:both;}
And the HTML becomes:
<div id="sub-title">
<div id="sub-left">Right</div>
<div id="sub-right">Left</div>
<div id="sub-close"></div>
</div>
Sorry, just realized this was posted previously, shouldn't have made that cup of coffee while typing my reply!
@Darko Z: you are right, the best description for the overflow:auto (or overflow:hidden) solution that I have found was in a a post on SitePoint a while ago Simple Clearing of FLoats and there is also a good description in a 456bereastreet article CSS Tips and Tricks Part-2. Have to admit to being too lazy to implement these solutions myself, as the closing div cludge works OK although it is of course very inelegant. So will make an effort from now on to clean up my act.