How do I create the small icon next to the website tab for my site?
It is called favicon.ico and you can generate it from this site.
http://www.favicon.cc/
This is for the icon in the browser (most of the sites omit the type):
<link rel="icon" type="image/vnd.microsoft.icon"
href="http://example.com/favicon.ico" />
or
<link rel="icon" type="image/png"
href="http://example.com/image.png" />
or
<link rel="apple-touch-icon"
href="http://example.com//apple-touch-icon.png">
for the shortcut icon:
<link rel="shortcut icon"
href="http://example.com/favicon.ico" />
Place them in the <head></head>
section.
Edit may 2019 some additional examples from MDN