Do you mean the block which conatins the categories, links, etc.? If so, you probably need to modify the CSS which is controlling how your site is rendered. I recommend looking at some of the examples here and finding one that renders close to how you want your site. Then study the CSS for the menu section for ideas.
I think what you are asking is how to get the background for the menu to extend down to the bottom of the page even though the content is longer. This is a common request and development but it does take you straight into the heart of layout, css and legacy browser issues. A lot of folks use float for the menu. It may be old fashioned. It may be buggy. We know all that. But it is css 1 compliant. Now if that is you’re starting point then how to fix up the
There are two ways to go. One is a kind of cheat and one involves a whole lotta hacking if you want you site viewable in all browsers. The choices are either to use a graphic as a tiled background in two different colours or use one color to fill the midsection and tile the menu with a small bg color graphic either right or left as required. HTH.