Google hides the search query for the most part. some people have hacks, but seldom work, especially if you are logged into a browser AND logged into a Google product, like Gmail.
Link:
http://moz.com/blog/google-hides-sea...teboard-friday
So if you are trying to track by keywords to conversions, good luck. You can however get insights from Google webmaster tools as far as rankings and kws.
However... seems like you are asking if someone comes to your site, how do you know the PATH or pages in the process that lead to the conversion/goal/event? If you setup your GOALS in analytics, then you can look at the reverse path...
Under "Conversions" click "Goals" then click on "Reverse Goal Path" and that should give you the easy answer you are looking for.