How to delete Gmail account?

Here is how -

Sign into your Gmail account.
Click on Settings at the top-right of the page.
Click on Accounts tab and Google Account settings link.
Your Google account will be opened in a new window. Click on Edit link next to My products.
In the next page you will find number of options with links to remove a product or the whole service itself.
Choose the appropriate link and fill in the feedback form.

All the best!