How do you install a .MO (language file) to use as part of a theme?

You need to load_theme_textdomain() in your theme.

Place this in theme functions file:

function theme_init(){
    load_theme_textdomain('theme_name', get_template_directory() . '/languages');
}
add_action ('init', 'theme_init');

Then you put you language files in you theme /languages folder

you language files should be es_ES.mo and es_ES.po without the text domain at the front as the codex states File names such as: my_theme-sv_SE.mo will NOT work.