By creating a child theme and customising the CSS and/or template files via the child theme.
Do you have to create a child theme in order to style the archives?
For the Twenty Ten themes, yes. Or your changes will be over-written the next time you upgrade WordPress or the theme.
I have actually copied the 2010 theme so that wouldn’t happen. How do you theme the archives specifically? Since the 2010 theme uses loop.php pretty exclusively, I assumed you would style the archives in there but, I have not found any code for it.
The archives use loop.php by default (get_template_part( 'loop', 'archive' );
) so you would need to create a loop-archive.php file for your customised archive display.