How to add a new field in admin form using Block?

Although Magento recommends using ui_component for creating grid or form in admin, Magento core itself has multiple forms & grid which is created using block(Old technique). So let's see how to add a field using the block technique:

For this first, we need to locate the block class which contains _prepareForm() method. And then we will create the Plugin for this class.

Step 1: Add the below code to the di.xml file of the custom module.

<?xml version="1.0" ?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
	<type name="Magento\CheckoutAgreements\Block\Adminhtml\Agreement\Edit\Form">
        <plugin name="add_embassy_field" type="MageInsight\CheckoutAgreements\Plugin\Block\Adminhtml\Agreement\Edit\Form" sortOrder="1"/>
    </type>
</config>

Step 2: Create a new file inside your module plugin folder like MageInsight\CheckoutAgreements\Plugin\Block\Adminhtml\Agreement\Edit\Form.php

<?php

namespace MageInsight\CheckoutAgreements\Plugin\Block\Adminhtml\Agreement\Edit;

use MageInsight\Embassy\Model\Options\Embassy;
 
class Form
{
    protected $embassy;

    protected $_coreRegistry;

    public function __construct(
        \Magento\Framework\Registry $_coreRegistry,
        Embassy $embassy
    ) {
        $this->embassy = $embassy;
        $this->_coreRegistry = $_coreRegistry;
    }

    public function aroundGetFormHtml(
        \Magento\CheckoutAgreements\Block\Adminhtml\Agreement\Edit\Form $subject,
        \Closure $proceed)
    {
        $form = $subject->getForm();
        if (is_object($form)) {
            $fieldset = $form->getElement('base_fieldset');
            $model = $this->_coreRegistry->registry('checkout_agreement');
            $fieldset->addField(
                'embassies',
                'multiselect',
                [
                    'name' => 'embassies[]',
                    'label' => __('Embassies'),
                    'title' => __('EMbassies'),
                    'required' => false,
                    'values' => $this->embassy->toOptionArray(),
                    'value' => !empty($model->getData('embassies')) ? json_decode($model->getData('embassies'), true) : []
                ]
            );
        }
 
        return $proceed();
    }
}

Step 3: If you are adding a multi-select field, then the form submit will pass values in an array and we have to take care of this. In my case, I have added a Plugin for the beforeSave() which will take care of values every time the entity is saved by admin. Below is the code of that plugin. 

<?php

namespace MageInsight\CheckoutAgreements\Plugin\Model;

class Agreement
{
    public function aroundBeforeSave(
        \Magento\CheckoutAgreements\Model\Agreement $subject,
        \Closure $proceed
    ) {
        if (!empty($subject->getData('embassies'))) {
            $subject->setData('embassies', json_encode($subject->getData('embassies')));
        }

        return $proceed();
    }    
}

Conclusion: By following the above steps you will be able to save the values in the form and see the saved values in edit form. I have saved the values in JSON format because later it makes my work easy to filter using JSON_SEARCH queries.