So part of making sure that your site gets out there is proper branding and making sure that people associate an image with your brand or your site. A simple way is through your favicon, it is seen next to the url in most browsers. Now the trick with favicon's is that they are so small they tend to be somewhat hard put a logo or a good picture in, in other words, don't just put up anything as your favicon.
The standard size of a favicon is 16 x 16 px. Yeah its pretty small, so make sure you have very few colors and probably no text. Okay, so where do we go?
1. First thing to know is that your favicon is determined by your template, most templates come with the standard Joomla favicon.
2. So you need to get into your server (ftp, cpanel, etc.) you need to go to folders:
public_html >>templates>>YOUR TEMPLATE>>
3. Once you are inside of your templates folder you should see a file named favicon.ico
4. All that is left is for you to save your 16 x 16 image that has the suffix .ico and simply replace the one in your template folder.
Simple. Any questions, leave a comment.