To send emails in Node.js with the SendGrid API, first set up a development environment by installing Node.js and npm, creating a free SendGrid account, and setting an API key as an environment variable. Then, install the SendGrid helper library for Node and create an `index.js` file to use the SendGrid API to send emails. The code can be run using the `node index.js` command to verify that it works correctly, allowing developers to easily integrate email sending into their Node.js applications.