To build and send emails with React Email and SendGrid, you need a free SendGrid account with a verified sender and an API key, as well as Node.js installed. You can create a new email project by initializing a new Node.js application, installing dependencies, and scaffolding out directories and files. Then, you can build the email in JSX format using React Email components, such as `Text`, `Heading`, and `Container`. After that, you can compile the JSX file to JavaScript using Babel, configure the SendGrid API client with your credentials, and use the `render` function from React Email to turn the email into HTML. Finally, you can send the email using the SendGrid Node library by creating a script that runs the build process, loads environment variables, and executes the code to send the email.