Go to this site (link) where you can change your picture from gif, jpg, png, or bmp format into .ico format. It's rather easy to do it, just upload the picture you want and click "create icon". Than you have to upload your new icon picture to some hosting site that accepts the ico format. You can use Google Sites (link) for it. Click "create a new site" and give your site the name you want (if it is available). Than you can upload the picture in .ico format and save it. Now you have to copy the URL of your icon file. You can do it by clicking with the mouse right button over the picture and choosing "copy image location". If you haven't this command on the displayed menu, choose "properties". A small window will pop-up and you can select and copy the url of your file that is after Location:

It will look something like this:

http://sites.google.com/site/yoursitename/_/rsrc/1223337404841/Home/favicon.ico

Go back to your Blogger dashboard and under the Template tab, go to “Edit HTML”. Near the top you will see a line like this:

<title><data:blog.pageTitle/></title>

Copy and insert the following code below the line:

<link href=' Paste the URL of your icon file here ' rel='shortcut icon' type='image/vnd.microsoft.icon'/>

Save your template and open your blog to see your favicon working

That's all folks!