I wrote a blog post on how to remove the blogger attribute with a simple script . Due to emails reagarding options, i had to do some work to keep you updated with variety. Feel free to share other methods on your comments.
Note
You should understand what you are doing
Back up your blog so that in case you make any error you should be able to get everything in order.
Just follow each step carefully:
Method one :Using CSS
1. Login to blogger
2. Click on click on the blog you want to edit
3. click on Template( to the left where you have overview,post etc)
4. Click on the Customize just below the template.
5.On blogger template designer, click on Advanced
6. copy and Paste the following #Attribution1{display:none;}
7. Click on Apply to block and view your blog.
Method 2 Removing the blogger widget
1. Go to Blogger.com and login to your Blogger profile
2. Select your blog that you wish to remove this attribute
3. Now go to template
4. click edit HTML
5. Click on “jump to widget”and select Attribution1 on the drop down .
6. Click Ctrl+F and paster this in the saerch box
7. Now you will see this code displayed. Replace true by false.
8.Click Save
9. Go to blog layout(one the left, where you clicked template)
10. Click the attribution Gadget and click remove in the pop up window.
Sorry for no screen shots. Blogging on my nokia Asha.