What are favicons?
Favicons are small 16x16 icon files that are displayed next to the URL of your site in a browser's address bar. Additionally they're often displayed next to the name of your site in a user's list of open tabs and bookmark listings making it easier for the user to quickly identify amongst other sites.
There are a number of free websites where you can generate a favicon for free.
Select the website that you'd like to use, and follow the instructions they give you.
For example, if you're using the Favicon Generator, you will be faced with this page.
This is where you can upload your logo icon that you'd like to use, or simply choose one from their free public gallery.
Once you've done that, you can press "Create Favicon" and it will take you to the next page.
This is where you need to click on the "Download the generated favicon" text to save your icon.
You can then send it to your website designer to upload for you.
It will then appear next to your URL like the example ones below.