You would first need to have an icon which you would like to use, bearing the extension .ico format. If you search your hard disk, you might find some images you like for your favicon.Now you would have to convert them to .ico format.How to do it.
How about the step to do that? this are the steps :
1. First you must have an image any .png,.jpeg,.gif format.
2.After that, you must change your image to be icon. For do that, you can use favicon Generator, please check out Favicongenerator or Dynamicdrive site to convert your image into icon format.
3.Browse your image there from your hard disk,click generate button and then downlaod your icon to your hard drive from there.
4.Now upload the icon to your any hosting service you use like,get it from here.where to upload files.
5.After uploading take the url of the image where it's hosted.
6.Now Login To Blogger and Browse to Layout > Edit/Html > Press Ctrl+F
Now Search For <head> and place the below code after this tag
<link rel="shotcut icon" href="Url OF The Image Hosted"/>