You can access a media URL from a Twilio MMS message using the MediaUrl properties in the webhook request, or by accessing the Message Resource and building the media URL manually. To use the manual method, you need to fetch the Message Resource and extract the URI of the Media resource, then remove the ".json" extension and prepend "https://api.twilio.com". This can be done using the Twilio REST API or with a JavaScript application that receives an MMS message, such as an Express.js app. The manual method allows for more flexibility in handling different types of media URLs.