Commercial Web HostingEdit
The best scenario is if you have access to a commercial (perhaps free) web hosting service. Most likely it supports PHP and MySQL "out of the box"; it's pretty standard these days. The downside is, unless you have shell access and are comfortable with text-mode text editors, you will have to FTP your PHP scripts to the server every time you make any changes (that will be very often), this gets very annoying after a while. If your desktop is running on Windows, I suggest you download the text editor editplus, which can open a file over FTP and whenever you save, upload automatically to the FTP site. A good open source alternative is jEdit, which can open and save automatically over FTP and even SFTP (secure) if one installs the FTP plugin. jEdit is written in Java, so it runs on Mac OS X, OS/2, Unix, VMS and Windows. For you Linux people, you can also use something like CurlFtpFS (http://curlftpfs.sourceforge.net/), which lets you mount an FTP location as if it were any other mountable object, and thus all those nasty file transfers are done transparently, and you can use any editor you want. If you're blessed with a shell account, but are equally lazy, SSHFS (http://fuse.sourceforge.net/sshfs.html) is the one for you (assuming you use SSH to access your account...)
Please remember that anytime you upload an executable script to your web site, you create an opportunity for a malicious user to exploit any vulnerabilities in your code. In fact, one of the major advantages of operating on a commercial web host's server is that your scripts are prevented from affecting many critical parts of the machine. As long as you do not store important information on your web site, any damage a malicious user could cause will be kept to a minimum.
Some web hosting companies offer different features but most have a purchased product that allows you to navigate your server space quite easily. It is called cPanel and it is a great way to learn how to either start web designing or become an advanced web designer/programmer. Plesk is similar in nature.