Today, you made an important decision. You want to get rid of your Gmail Account. Whatever your reason is, one thing is for sure, you are not satisfied with it that you decided to delete it. When you were browsing Gmail though, you realized that you can't find any page where you can delete the account, and that is really frustrating. But don't worry now because deleting your Gmail account is really easy, and you just need to be directed to the right pages.  

First you have to login to https://www.google.com/accounts/.

In the page that shows, you will see an information about your account and the products that you are using from Google, these products like Gmail is listed on the right side / column of your screen. 

On the right column, where it says My Products, there is the Edit Link.  Click that link and you will be redirected to a page where you have the option to delete Google products you are using. One of the link should say "Delete Gmail Service." Click this link. 

On the next page, read carefully the warning from Google. If you are sure of deleting your account, just check the box for:  

"Yes, I want to permanently delete xxxxx@gmail.com and remove from my Google account." 

It will take two business days before your Gmail account will be deleted permanently. If you are using other Google products, you have to add another email address so that you can still access them.

But just a suggestion, if you are deleting your Gmail account because you are annoyed of getting messages from someone you don't like, why don't you just customize your Gmail account to not receive the emails from this person?