This is a very frequently asked question by the beginners with blogger.Even when I was a newbie I was also confused about it.
So I've decided to write a step-by-step tutorial on "How to change your Blogger Template ?".
Step I - Dashboard > Layout > Edit HTML.
Step II - Always backup your old template by downloading it. Click "Download Full Template".
Step III - Now backup all your widgets (page elements) by copying the code and pasting it on any text file.
Step IV - Now click on the Browse tab , just below it. Select the your favourite Template file (always with .xml extension) and press Upload.
Step V - If you are having any page elements in your old templates, the Blogger will remind you that you are about to delete them. Just click "Confirm & Save".
That's it you have successfully changed your blogger template and you see how it looks by clicking "View Blog".
Note : If you are having error with this method ,you can just copy the HTML code from New Templates .xml file and paste it in the text box at "Edit HTML" page after checking the "Expand
Widget Templates" box ,instead of Step IV.