widget with boarder image

The answer depends entirely on your theme. For example, in the Twenty Ten theme, you would add this to the end of a child theme’s style.css:

.widget-container {
   border: 2px solid #00FF00;
   padding 5px;
}

This would give you a 2px wide, solid green border with 5px of padding between the border and the content.

If you have a free theme, post a link to it here and you may get more specific information. If you have a purchased theme, you should contact the theme’s supplier.