You can set up an external email provider on Strapi Cloud using Sendgrid by following a series of steps including verifying your domain-specific email, creating an API key, installing the `@strapi/provider-email-sendgrid` provider, configuring it with your API key and verified email address, setting environment variables in your `.env` file, pushing the changes to Strapi Cloud, and updating the variables on Strapi Cloud. Once these steps are completed, you can use your custom SendGrid email provider to send emails through your Strapi application. The process allows for seamless integration of external email services with Strapi Cloud, enabling users to boost their team's velocity and enhance their project's functionality.