How to make my new theme read [youtube id=”id of the video here” width=”600″ height=”350″]?

You can for example:

• Copy the YouTube shortcode from the old theme to your new theme.

  Locate the line (most likely in the functions.php file):

  add_shortcode( 'youtube', 'some_function' );
  

  and copy this line and the some_function() to your functions.php in your new
  theme or better yet – create a new plugin file including:

  /*Plugin Name: YouTube embed shortcode from old theme */
  
  add_shortcode( 'youtube', 'some_function' );
  
  some_function( $args = array(), $content=""){ /* ...code... */}
  

• Add a YouTube embed plugin with the same parameters.

• Create your own plugin to handle this.

  Here’s a poor man’s version (untested):

  /*Plugin Name: YouTube embed shortcode - poor man's version */
  
  add_shortcode( 'youtube', 'ytb_sc' );
  
  if( ! function_exists( 'ytb_sc' ) ):
  
      function ytb_sc( $atts = array(), $content="" )
      {
         $atts = shortcode_atts( array(
             'id'      => '',             // default id
             'width'   => 640,            // default width (px)
             'height'  => 480,            // default height (px)
         ), $atts, 'ytb_sc' );
  
           // Sanitize input:
           $id      = esc_attr( $atts['id'] );
           $width   = (int) $atts['width'];
           $height  = (int) $atts['height'];
  
          if( ! empty( $id ) ) {
              $sc = sprintf( '%s%s',
                             $width,
                             $height,
                             'https://www.youtube.com/watch?v=',
                             $id );
          } else {
              return __( 'Missing YouTube ID!' );
          }
  
          // Output
          return $GLOBALS['wp_embed']->run_shortcode($sc);
      }
  
  endif;
  

Hope this helps!