This article explains how to buy airline tickets with Google Flights. There are two ways to use Google Flights: Search for airline tickets directly through the search engine or go to the Google Flights website to find tickets.
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Google Flights searches flight prices without ever leaving the Google search engine. You can see which airlines you can choose from, select a specific departure and arrival date, and see prices right in the search results.
For example, you can open a new Google search and type "flights from MCI to NYC in October" to tell Google to find flights that meet that specification. Or, if your browser has access to your current location, you can simply type "flights to New York City" to get information about airfares related to the airport closest to you.
If you use the Google Flights website, you will not only see a list of flights, but also a map of them on the right, along with your current location. From there, you can change the number of passengers flying; choose from first class, economy, etc.; view flights within a flexible time frame; filter the results by many different criteria.