The platform you need to access to get your free API key is Google AI Studio.
Here are the details and the direct URL:
Google AI Studio Access Details
Key Generation Process
Once you log in using the URL above, the process is streamlined:
Sign In: Use your Google account credentials. Review Terms: You will be prompted to read and accept the terms of service. Create Key: On the API keys dashboard, click the "Create API Key" button. Copy: Your unique key string will be generated instantly. Copy this key immediately and store it safely, as you will not be able to view the full string again. This key is what you will use to set the GEMINI_API_KEY environment variable needed to run the Node.js application.
The URL for getting the API key is not gemini.google.com. That site is for the consumer-facing chat application.
The correct and most direct URL for generating the free developer API key is:
https://aistudio.google.com/app/apikey
Once you log in with your standard Google Account at that link, you'll be taken straight to the page where you can generate your key under the generous free tier.