To regulate pop-ups in Microsoft Edge, users can block or allow pop-ups for specific sites, managing their browsing experience. To block pop-ups, users turn on the 'Block' toggle under the 'Blocker (recommended)' section, while to allow pop-ups for a site, they enable it by turning off the 'Block' toggle and adding the site URL to the 'Allow' section. Additionally, users can identify malware or phishing pop-ups by looking for urgent messages, untrusted URLs, and requests for sensitive information, and block them on Edge Android by disabling "Allow pop-ups" in Edge Settings.