How do I redirect /search/ to wordpress search template?

You can use template_redirect. Here a simple redirection function.

add_action( 'template_redirect', 'se219663_template_redirect' );

function se219663_template_redirect()
{
  global $wp_rewrite;

  if ( is_search() && ! empty ( $_GET['s'] )  )
  {
    $s         = sanitize_text_field( $_GET['s'] ); // or get_query_var( 's' )
    $location  = "https://wordpress.stackexchange.com/";
    $location .= trailingslashit( $wp_rewrite->search_base );
    $location .= user_trailingslashit( urlencode( $s ) );
    $location  = home_url( $location );
    wp_safe_redirect( $location, 301 );
    exit;
  }
}

Rule without search query, like this ( don’t forget go to Permalink Settings to flush the rules ):

add_filter( 'search_rewrite_rules', 'se219663_search_rewrite_rules', 10, 1 );
function se219663_search_rewrite_rules( $rewrite )
{
  global $wp_rewrite;
  $rules = array(
    $wp_rewrite->search_base . '/?$' => 'index.php?s=",
  );
  $rewrite = $rewrite + $rules;
  return $rewrite;
 }

and redirect with empty search query, just use isset, modified from the code above.

add_action( "template_redirect', 'se219663_template_redirect' );

function se219663_template_redirect()
{
  global $wp_rewrite;

  if ( is_search() && isset ( $_GET['s'] )  )
  {
    $s         = sanitize_text_field( $_GET['s'] ); // or get_query_var( 's' )
    $location  = "https://wordpress.stackexchange.com/";
    $location .= trailingslashit( $wp_rewrite->search_base );
    $location .= ( ! empty ( $s ) ) ? user_trailingslashit( urlencode( $s ) ) : urlencode( $s );
    $location  = home_url( $location );
    wp_safe_redirect( $location, 301 );
    exit;
  }
}