"This sounds weird, but how do I delete my google account?"
Strangely, I too had some problems when I first tested deleting a Google Account as it was not as straight forward as I thought. So here is a step-by-step instruction on how to delete your Google Account. Warning: Deleting your Google Account means you will not be able to access your Blogger account, gmail account or whatever Google Products you have signed up for. So be absolutely sure you don't ever want to access those accounts again later before you delete your Google Account.
First, sign into your Google Account. Then, next to My Products, click Edit.

At the next page, under Delete Account, click Close account and delete all services and info associated with it.

At the next page, tick all the services and products shown and enter your password.

Click Delete Google Account and your Google Account will be gone almost forever.
Related posts:
How to recover deleted Google Account (not fool proof)
Google Account deleted, cannot access Blogger.com, what to do