An API key can be gotten by visiting https://developers.google.com/places/web-service/get-api-key, scrolling to the Get an API key section, and clicking the GET A KEY button:
Upon clicking the button, you will be presented with a modal from which you can select or create a project to be integrated with the Google Places API Web Service. Click on the dropdown and select Create a new project. You will be requested to provide a project name. Input Place Reviewer as the project name:
After providing a project name, click NEXT ...
