If you are using the old interface, please read this post on removing Powered by Blogger in old Blogger interface.
Please backup your blogger template before you make any changes to it. This helps to revert back to the original template when something goes wrong while editing your template. The steps for backup and restore are discussed here in detail.
Steps to remove the Powered by Blogger text from your blog in the new Blogger interface:
1. Click on the Template link in the left navigation menu.
2. Click on the Edit HTML button
4. Remove the following highlighted code.
6. A warning is displayed.Click on Delete Widgets and click on Save Template Button.