First of all, we need to define the action node in your ui xml.

<?xml version="1.0" encoding="UTF-8"?>
<!--
/**
 * Copyright © 2015 Magento. All rights reserved.
 * See COPYING.txt for license details.
 */
-->
<listing xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Ui:etc/ui_configuration.xsd">
    ......
   
    <columns name="rent_columns">
        ......
        <actionsColumn name="actions" class="Vendor\Module\Ui\Component\Listing\Column\Actions">
            <argument name="data" xsi:type="array">
                <item name="config" xsi:type="array">
                    <item name="indexField" xsi:type="string">entity_id</item>
                </item>
            </argument>
        </actionsColumn>
    </columns>
</listing>

Build the action class:

app/code/Vendor/Module/Ui/Component/Listing/Column/Actions.php

<?php

namespace Vendor\Module\Ui\Component\Listing\Column;

use Magento\Framework\View\Element\UiComponent\ContextInterface;
use Magento\Framework\View\Element\UiComponentFactory;
use Magento\Ui\Component\Listing\Columns\Column;
use Vendor\Module\Block\Adminhtml\Module\Grid\Renderer\Action\UrlBuilder;
use Magento\Framework\UrlInterface;

class Actions extends Column
{
    /** Url path */
    const URL_PATH_EDIT = 'your/url/edit';
    const URL_PATH_DELETE = 'your/url/delete';

    /** @var UrlBuilder */
    protected $actionUrlBuilder;

    /** @var UrlInterface */
    protected $urlBuilder;

    /**
     * @param ContextInterface $context
     * @param UiComponentFactory $uiComponentFactory
     * @param UrlBuilder $actionUrlBuilder
     * @param UrlInterface $urlBuilder
     * @param array $components
     * @param array $data
     */
    public function __construct(
        ContextInterface $context,
        UiComponentFactory $uiComponentFactory,
        UrlBuilder $actionUrlBuilder,
        UrlInterface $urlBuilder,
        array $components = [],
        array $data = []
    ) {
        $this->urlBuilder = $urlBuilder;
        $this->actionUrlBuilder = $actionUrlBuilder;
        parent::__construct($context, $uiComponentFactory, $components, $data);
    }
    /**
     * Prepare Data Source
     *
     * @param array $dataSource
     * @return array
     */
    public function prepareDataSource(array $dataSource)
    {
        if (isset($dataSource['data']['items'])) {
            foreach ($dataSource['data']['items'] as & $item) {
                $name = $this->getData('name');
                if (isset($item['entity_id'])) {
                    $item[$name]['edit'] = [
                        'href' => $this->urlBuilder->getUrl(self::URL_PATH_EDIT, ['entity_id' => $item['entity_id']]),
                        'label' => __('Edit')
                    ];
                    $item[$name]['delete'] = [
                        'href' => $this->urlBuilder->getUrl(self::URL_PATH_DELETE, ['entity_id' => $item['entity_id']]),
                        'label' => __('Delete'),
                        'confirm' => [
                            'title' => __('Delete ${ $.$data.title }'),
                            'message' => __('Are you sure you wan\'t to delete a ${ $.$data.title } record?')
                        ]
                    ];
                }
            }
        }
        return $dataSource;
    }
}

Url builder class:

app/code/Vendor/Module/Block/Adminhtml/Module/Grid/Renderer/Action/UrlBuilder.php

<?php

namespace Vendor\Module\Block\Adminhtml\Module\Grid\Renderer\Action;

class UrlBuilder
{
    /**
     * @var \Magento\Framework\UrlInterface
     */
    protected $frontendUrlBuilder;
    /**
     * @param \Magento\Framework\UrlInterface $frontendUrlBuilder
     */
    public function __construct(\Magento\Framework\UrlInterface $frontendUrlBuilder)
    {
        $this->frontendUrlBuilder = $frontendUrlBuilder;
    }
    /**
     * Get action url
     *
     * @param string $routePath
     * @param string $scope
     * @param string $store
     * @return string
     */
    public function getUrl($routePath, $scope, $store)
    {
        $this->frontendUrlBuilder->setScope($scope);
        $href = $this->frontendUrlBuilder->getUrl(
            $routePath,
            ['_current' => false, '_query' => '___store=' . $store]
        );
        return $href;
    }
}