You can add scrollbars to a div with this code. The scrollbar will automatically appear if the content is too large to fit.
div.content
{
overflow: scroll;
}
This will only get you halfway, since you also need to set the height of the content div so that the whole page has a height of 100 %. It is my experience, that you are opening a big bag of browser compatibility problems if you try to use height: 100%. You could also use JavaScript to set the height of the div on document.load and document.resize, but that would give a small but noticeable flicker when the page loads.
I think the best solution would be to overlay the header and the footer over the content of the page and make their positions fixed. This would attach the scrollbar to the window and not the div tag, making it full height, so it might not be what you want. There is a nice example on how to accomplish this here: Fixed header and footer.