If you want to know how people find your website purely through google search, you can make use of Google Analytics.

 First, you login to your Google Analytics account. Then you goto the Traffic Sources on the left menu. Choose Search Engines. The main area will show you a list of all the search engines that are sending you traffic. If you click on Google and you will see a keyword list of all the keywords used to find your site via Google.

If you add keywords through your Google Adwords, you may want to combine Google analytics and Google Adwords to give you the best value for money. Below is a Google video that shows you how to do it.