My guess is that you're using either rwd theme or some derivate of it (different theme implement such things differently). In app/design/frontend/rwd/default/layout folder there's a file catalog.xml there's block that looks like this:
<block type="catalog/product_view_attributes" name="product.attributes" as="additional" template="catalog/product/view/attributes.phtml">
<action method="addToParentGroup"><group>detailed_info</group></action>
<action method="setTitle" translate="value"><value>Additional Information</value></action>
</block>
What you need to do is to add attribute before="-" to the first block definition. Like this:
<block type="catalog/product_view_attributes" before="-" name="product.attributes" as="additional" template="catalog/product/view/attributes.phtml">
<action method="addToParentGroup"><group>detailed_info</group></action>
<action method="setTitle" translate="value"><value>Additional Information</value></action>
</block>
Before attribute means that this block must be rendered before another block. "-" means that this must be rendered before everything else. There's a possibility that some of the other tab definitions have this attribute attached, but it's unlikely. You can also switch product blocks named product.attributes and product.info.additional if you want.
As I mentioned before your tab definitions could be different, as different themes are different. They are not THAT different, so hopefully it gives you an idea where to look and what to do.
Tanel Raja