How do I change the fonts in the Twenty Thirteen theme?

I looked at TwentyThirteen’s twentythirteen_fonts_url() function and there are no hooks so you need to
deregister twentythirteen-fonts and enqueue your own fonts.

Removing the fonts is easy:

function deregister_gfonts_wpse_111190() {
  wp_deregister_style('twentythirteen-fonts');
}
add_action('wp_enqueue_scripts','deregister_gfonts_wpse_111190',100);

Add your own Google fonts (or other) the same way that TwentyThirteen did.

You will need to add another stylesheet to override the places where TwentyThirteen uses the fonts though.