How to enqueue the style using wp_enqueue_style()

I’m developing a theme. I added the codes (below) into the header.php. But I posted it into the WP theme repository, and it’s under review, and the reviewer informed me to enqueue the style with wp_enqueue_style()/ wp_enqueue_script(). But can’t understand how to implement it with the function. I’ve seen the directed wp_enqueue_style(); in Codex, but can’t understand how to put the whole bunch of codes with their conditions.