When logged on to Gmail select the blue circle in the top right, then select Account which shows your account settings.
Scroll to the bottom and select the option Delete Google Account and Data
Note all these companies do supply help and a simple search on the internet for "delete gmail account" (or similar phrases) will usually give you an answer, like this one
. . . and if you want a better free email service (which doesn't try to tie you to Google or, indeed, to anything else) look no further than here:
http://www.gmx.co.uk/