An example of dequeueing a parent theme (in this case TwentyTwelve) to include your own.
function replace_twentytwelve_styles() {
wp_dequeue_style( 'twentytwelve-style' );
wp_deregister_style( 'twentytwelve-style' );
wp_enqueue_style( 'my-style', get_stylesheet_directory_uri() . '/css/style.css' );
}
add_action( 'wp_enqueue_scripts', 'replace_twentytwelve_styles', 11 );