Magento 2 How to create new order attribute programatically

Practically, there are two main ways to add an order attribute (a new column) to order via an upgrade script.

--Using $setup->getConnection()->addColumn()

app/code/Vendor/SalesOrder/Setup/UpgradeSchema.php

<?php

namespace Vendor\SalesOrder\Setup;

use Magento\Framework\Setup\UpgradeSchemaInterface;
use Magento\Framework\Setup\SchemaSetupInterface;
use Magento\Framework\Setup\ModuleContextInterface;

class UpgradeSchema implements UpgradeSchemaInterface
{
    /**
     * Upgrades DB schema for a module
     *
     * @param SchemaSetupInterface $setup
     * @param ModuleContextInterface $context
     * @return void
     */
    public function upgrade(SchemaSetupInterface $setup, ModuleContextInterface $context)
    {
        $setup->startSetup();

        $quote = 'quote';
        $orderTable = 'sales_order';

        $setup->getConnection()
            ->addColumn(
                $setup->getTable($quote),
                'custom_attribute',
                [
                    'type' => \Magento\Framework\DB\Ddl\Table::TYPE_TEXT,
                    'length' => 255,
                    'comment' =>'Custom Attribute'
                ]
            );
        //Order table
        $setup->getConnection()
            ->addColumn(
                $setup->getTable($orderTable),
                'custom_attribute',
                [
                    'type' => \Magento\Framework\DB\Ddl\Table::TYPE_TEXT,
                    'length' => 255,
                    'comment' =>'Custom Attribute'
                ]
            );

        $setup->endSetup();
    }
}

--Using Quote and Sale Setup Factory

app/code/Vendor/SalesOrder/Setup/UpgradeData.php

<?php

namespace Vendor\SalesOrder\Setup;

use Magento\Framework\Setup\ModuleContextInterface;
use Magento\Framework\Setup\ModuleDataSetupInterface;
use Magento\Framework\Setup\UpgradeDataInterface;
use Magento\Quote\Setup\QuoteSetupFactory;
use Magento\Sales\Setup\SalesSetupFactory;

class UpgradeData implements UpgradeDataInterface
{
    /**
     * @var QuoteSetupFactory
     */
    protected $quoteSetupFactory;

    /**
     * @var SalesSetupFactory
     */
    protected $salesSetupFactory;

    /**
     * @param QuoteSetupFactory $quoteSetupFactory
     * @param SalesSetupFactory $salesSetupFactory
     */
    public function __construct(
        QuoteSetupFactory $quoteSetupFactory,
        SalesSetupFactory $salesSetupFactory
    ) {
        $this->quoteSetupFactory = $quoteSetupFactory;
        $this->salesSetupFactory = $salesSetupFactory;
    }
    /**
     * Upgrades DB for a module
     *
     * @param ModuleDataSetupInterface $setup
     * @param ModuleContextInterface $context
     * @return void
     */
    public function upgrade(ModuleDataSetupInterface $setup, ModuleContextInterface $context)
    {
        /** @var \Magento\Quote\Setup\QuoteSetup $quoteInstaller */
        $quoteInstaller = $this->quoteSetupFactory->create(['resourceName' => 'quote_setup', 'setup' => $setup]);

        /** @var \Magento\Sales\Setup\SalesSetup $salesInstaller */
        $salesInstaller = $this->salesSetupFactory->create(['resourceName' => 'sales_setup', 'setup' => $setup]);

        $setup->startSetup();

        //Add multiple attributes to quote 
        $entityAttributesCodes = [
            'custom_attribute' => \Magento\Framework\DB\Ddl\Table::TYPE_TEXT,
            'custom_attribute1' => \Magento\Framework\DB\Ddl\Table::TYPE_TEXT

        ];

        foreach ($entityAttributesCodes as $code => $type) {

            $quoteInstaller->addAttribute('quote', $code, ['type' => $type, 'length'=> 255, 'visible' => false, 'nullable' => true,]);
             $salesInstaller->addAttribute('order', $code, ['type' => $type, 'length'=> 255, 'visible' => false,'nullable' => true,]);
            $salesInstaller->addAttribute('invoice', $code, ['type' => $type, 'length'=> 255, 'visible' => false, 'nullable' => true,]);
        }

        $setup->endSetup();
    }
}

Magento 2.3.4 do not support above format:

Please check below steps to add new attribute to sales_order, quote and sales_invoice tables.

Vendor/Module/etc/db_schema.xml

<?xml version="1.0"?>

<schema xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
        xsi:noNamespaceSchemaLocation="urn:magento:framework:Setup/Declaration/Schema/etc/schema.xsd">
    <table name="sales_order" resource="sales" engine="innodb" comment="Sales Order">
        <column xsi:type="varchar" name="note" nullable="true" length="255" comment="Note"/>
    </table>
    <table name="quote" resource="checkout" engine="innodb" comment="Quote">
        <column xsi:type="varchar" name="note" nullable="true" length="255" comment="Note"/>
    </table>
    <table name="sales_invoice" resource="sales" engine="innodb" comment="Sales Invoice">
        <column xsi:type="varchar" name="note" nullable="true" length="255" comment="Note"/>
    </table>
</schema>

After that please run php bin/magento setup:upgrade command.