That PHP code you're complaining about? That's what creates the connection to the database. PHP is a server-side scripting language. As requests come to the server, the PHP code executes, creates a connection to the database, queries the database based on whatever filtering you're asking the PHP script to do, captures the returned data from the quire to the database, puts it all back together and displays it as HTML on your page.
You really shouldn't "connect" your database directly to a website - that would be a security nightmare! Instead, you use server-side scripting langauge (PHP or ASP .NET are the big ones) to make carefully controlled and paramaterized calls (queries) to the database and return the data appropriately formated for display.
As for a testing server, take a look at WAMP/MAMP/XAMP - basically Apache, MySQL and PHP for W(indows), M(ac). It creates a nice self-contaioned environment on your local machine for testing. Testing servers are great because you can test your ideas in a nice, controlled environment before releasing them into the wilds of the internet. And with databases, you really do want to test things and make sure to lock stuff down - again there can be serious security implications once you start developing dynamic web sites.
