As you know that Google's blogger.com which is widely known as blogspot has changed its template. With this template the features look different and that's why bloggers might find it difficult of one needs to look for the right button for a long time.
Here is how to delete a blog both blogspot or customized one.
1. Go to the "setting" of the blog you want to delete. You will find setting when you click the blog title or the drop down button on the right hand side of the title. Note: Setting is the last option there.
2.Go to the "other" under setting.
3. Look for "Blog tools" at the top of the page.
4. Click "Delete Blog"
5. Click "Delete this Blog"
Warning: Please make sure you are deleting the one you want to delete. Good luck