What is the easiest way to create an HTML, mouse over tool tip?

The easiest way is to use the native HTML title attribute:

<img src="https://stackoverflow.com/favicon.ico"
     style="cursor:pointer;"
     title="Stack Overflow">

But if you need more, try the tooltip widget provided by jQuery UI since version 1.9.

If you don't care much what the tooltip looks like you can always just use the "title" attribute