I just recently installed Joomla! using a database that already had an instance of Joomla! installed in it. It was actually really easy. This article explains how to install multiple instances of Joomla! with 1 database.
Why is this useful?
These days, you can find affordable hosting providers that allow you to run as many MySQL databases as you need. The only limitation is the amount of space they take up. However, there are still some hosting providers out there that only allow 1 MySQL database per hosting account. If you want to run 2 or 3 Joomla! sub sites on your account, you have to be able to install all instances of Joomla! on the one database. Luckily, Joomla! makes a provision for this possibility.