To allow users to upload media files to the cloud, developers can use Twilio Verify to generate one-time passcodes delivered to users' mobile phones and Amazon Simple Storage Service (Amazon S3) to store the files. The application uses Flask to create a web interface that allows users to enter their email address, receive a verification code via SMS or phone call, and upload an image file in .jpg, .png, or .jpeg format. After uploading the file, it is stored in the project directory's "UPLOADS" folder and then uploaded to the S3 bucket using boto3 library. The application also includes measures to protect user data, such as secure password handling and two-factor authentication.