Welcome to the MacNN Forums.

I have downloaded Firefox 2.0.0.14 and am using it. It has created an icon on my desktop that looks like my CD/DVD drive. I have the program on the dock and it works fine, but the desktop icon won't go away. What is that all about?

Close Firefox.

Now open what looks like a CD/DVD drive (it's called a disk image). Note that Firefox is on that disk image. Drag it into your Applications folder on your hard drive. For your convenience the disk image should already contain an alias to your Applications folder which you can use to drop Firefox onto. Now drag the disk image drive onto the trash to eject it. You can also trash the disk image file now (ending with .dmg).

From now on launch Firefox from your Applications folder. You can keep that copy in your Dock (and you might have to remove the one you had in the Dock previously from the Dock since it's now pointing to a copy of Firefox that's no longer there).

Installing programs on Mac is "easy" thanks to Apple. Now you can do it too.

Thanks for your help. Is this a common installation issue? I've installed on other application, but it seemed to go where it should.

Yes, that's the normal installation process for Mac OS X applications.

Adium, Camino, Google Earth and Skype are all examples of applications that are installed like this (iirc).