One way to do it would be via the local.xml in /app/design/frontend/yourpackagename/yourthemename/layout/local.xml. The handles that you need to add depend on how your checkout process is configured. Here is some example code to get you started:
<checkout_cart_index>
<remove name="footer">
</checkout_cart_index>
<checkout_onepage_index>
<remove name="footer">
</checkout_onepage_index>
This is removing the entire footer block, but you can use it to remove any block name that you have. Alan Storms layoutviewer module is great for figuring out what the layout handles are: http://alanstorm.com/layouts_blocks_and_templates.