If you're not automatically logged in, click on Sign In in the upper right, and enter your Google username and password. The window will open to the main screen of your most-recently accessed blog. It's located to the right of your blog's title, just below the Blogger logo in the upper left of the window. All of your Blogger blogs will appear in the drop-down you just opened. Only owners or admins can delete a blog. It's near the bottom of the menu on the left side of the window. You may have to scroll down to see it. It's near the bottom of the sub-menu that opens under Settings. It's on the right side of the screen, in the second section of options. If you want to save a copy of your blog, click Download Blog in the dialog box that pops up. Your blog has been deleted from your Blogger account. You'll have 90 days to change your mind and restore the blog. You can do so from the Deleted Blogs list in the drop-down menu of your Blogger blogs.
Go to Blogger. Click on ▼. Click on the blog you wish to delete. Click on Settings. Click on Other. Click on Delete Blog. Click on Delete This Blog.