Before you add an API key, you have to grant Goldie access to Google's servers by adding a Remote Site setting:
In Salesforce go to Setup and find the page "Remote Site Settings".
Click the button "New Remote Site"
Add a new remote site called "Google_Gemini" with the URL https://generativelanguage.googleapis.com
Click "Save".
Create or login to a Google AI Studio account at https://aistudio.google.com.
If asked, select "Build with the Gemini API".
Open this URL: https://aistudio.google.com/apikey
Click the button "Create API key" and generate a new API key in an existing project.
After clicking "Create API key" the modal "API key generated" displays the new key. Copy the API key to the clipboard and leave this modal open for now.
In Salesforce click on the App Launcher and find the item "Goldie Setup".
In the Goldie Setup Page find the section "AI Model Settings".
Select a Google Gemini Model.
Click the button "Edit LLM API Key" and paste the API key from before into the text box of the modal.
Click the button "Test OpenAI Connection". The button should turn green.