The Zapier Chrome extension is a tool that allows users to add new rows to their Google Sheets with the click of a button while browsing the web, without needing to open the sheet itself. To set up the extension, users need to create or label their columns, install and pin it in the Chrome store, log in to their Zapier account, and create a two-step Zap that captures URLs from the Chrome extension and maps them to specific fields in the Google Sheet. The extension offers various features such as dynamic values, field mapping, testing, and returning responses to users, making it easy to automate tasks and track information without manual effort.