The "Y" on Yumarama.com and the little loaf logo on this site are called "FavIcons". If you Google that, you'll get links to website3s where you can upload a graphic of your own and they produce a favicon.ico file of it, instantly and free. You then upload that file to your site's main directory and it should show up automatically.
The final product is a small, 16 X 16 pixel somewhat coarse version of your original graphic so make that original you upload (even if it's a smaller version of your normal one) as clean looking as possible as small as possible. It will be resized to the right size. And the final product is a square graphic so don't try to use something decidedly vertical or horizontal or it will get squished down too small to see properly.
People who have visited your site before the icon was uploaded may need to refresh their browser to pick it up else they may (or may not, depends more on their browser than anything else) just see the generic default icon in the URL bar and their Favourites/Bookmarks folders.
I do not know if this would work on Wordpress.com although it has nothing to do with whether a site is a blog or anything else. But if you have a Blogger or Wordpress.com blog site or some such hosted domain, they may not let you do this. You'll just have to give it a shot or check their FAQs.