Step 1: Create an 16 pixels by 16 pixels image, save it in gif or png format.

Step 2: Go to an icon generating websites and convert your .gif/.png file to .ico file. (eg. http://tools.dynamicdrive.com/favicon/)

Step 3: Upload your generated .ico file to your server.

Step 4: Alter your blog template. Go to Blogger, Design, Edit HTML. Check the expand widget template checkbox.

Find </html> on your code. Paste this before the </html>. Remember to change the favicon url first.

<link rel="shortcut icon" href="YOUR-FAVICON-URL">
<link rel="icon" href="YOUR-FAVICON-URL">