It all depends a bit if your current theme already supports localization.
Does your theme’s function file contain something like this?
load_theme_textdomain( 'twentytwelve', get_template_directory() . '/languages' );
If not, add it in there. And change twentytwelve to your theme-directory-name.
After that create a directory called languages in the root of your theme a drop your localization file (theme-directory-name-sv_SE.mo) in there.