The "Magento way" to do something like this will vary depending on your site. You could edit the CSS as suggested - that's a simple band-aid fix that changes where the element is displayed, but not where it is. I would argue that if you wanted to use CSS to position the bottom of your webpage at the top (or somewhere else for that matter), why not just put it there instead of relying on smoke and mirrors?
What happens when the next guy comes along and tries to change the position of something else and not only wastes time realizing it was done with CSS but also now has to either shoe-horn his own changes into a negative margin or rewrite the previous changes making the previous effort a waste of time.
Learning how to use Magento's layout system will allow you to change placement of various page components more accurately and more predictably (especially for the next guy that works on the site). While it may depend on how your site is designed, finding the file: app/design/frontend/[your_theme/your_package/page/html/header.phtml (link to default file) will likely leave you with simply changing the position of:
<?php echo $this->getChildHtml('topMenu') ?>
You can likely just move that line in your template file to be the last line.