How do I add a text input field for customers to leave a note on a single WooCommerce product page?

The best way to extend WordPress and WooCommerce is by using hooks. To add custom option field on products area, you can use the following hooks:

• woocommerce_product_options_advanced: used to add a custom field into the Advanced Tab
• woocommerce_process_product_meta: used to save/update field data in the database

On your functions.php, you can add the following code:

/* create a new product field*/
add_action( 'woocommerce_product_options_advanced', 'personalization_product_options_adv' );
function personalization_product_options_adv() {
    echo '<div class="options_group">';

    woocommerce_wp_textarea_input( array( 
        'id' => 'product_personalization_note',
        'value' => get_post_meta( get_the_ID(), 'product_personalization_note', true ),
        'label' => 'Personalization Note',
        'desc_tip' => true,
        'description' => 'Allow product personalization for select products',
    ) );

    echo '</div>';
}

/* save & update the changes*/
add_action( "woocommerce_process_product_meta", "personalization_save_fields" );
function personalization_save_fields( $post_id ) {
    // grab the custom data from $_POST
    $product_personalization_note = isset( $_POST[ 'product_personalization_note' ] ) ? sanitize_text_field( $_POST[ 'product_personalization_note' ] ) : '';

    // grab the product
    $product = wc_get_product( $post_id );

    // save the custom data using WooCommerce built-in functions
    $product->update_meta_data( 'product_personalization_note', $product_personalization_note );

    //save
    $product->save();
}

/* display the new field on single product pages */
function woocommerce_custom_fields_display() {
  global $post;
  $product = wc_get_product($post->ID);
    $custom_fields_woocommerce_title = $product->get_meta('product_personalization_note');
  if ($custom_fields_woocommerce_title) {
      printf(
            '<div><label>%s</label><input type="text" id="woocommerce_product_custom_fields_title" name="woocommerce_product_custom_fields_title" value=""></div>',
            esc_html($custom_fields_woocommerce_title)
      );
  }
}
add_action('woocommerce_before_add_to_cart_button', 'woocommerce_custom_fields_display');

To retrieve this data in the frontend or emails sent by WooCommerce, you can use the regular get_post_meta() function like so:

$product_additional_note = get_post_meta( get_the_ID(), 'product_additional_note ', true );

Source:

• Extending WooCommerce Products With Custom Fields
• How to add custom fields to WooCommerce Product Data metabox