The background on the Yahoo Answers page is actually a very small image that is tiled across the whole page. So first you'd need to upload the image you want (let's call it 'bg.gif') to your themes "images" folder.
Then you'd need to edit your theme's default.css (line 6) and change:
body {
background-color:#F0F0F0;
color:#333333;
font-family:'Lucida Grande',Arial,Helvetica,sans-serif;
font-size:12px;
font-size-adjust:none;
font-stretch:normal;
font-style:normal;
font-variant:normal;
font-weight:normal;
height:100%;
line-height:normal;
min-height:100%;
}
to
body {
background:#F0F0F0 url(images/bg.gif);
color:#333333;
font-family:'Lucida Grande',Arial,Helvetica,sans-serif;
font-size:12px;
font-size-adjust:none;
font-stretch:normal;
font-style:normal;
font-variant:normal;
font-weight:normal;
height:100%;
line-height:normal;
min-height:100%;
}