What to do once a New Program is downloaded?

OpenOffice is different - it requires something called X11... You run the X11 environment and then start OO from there...it's a bit more complicated than that, but you get the idea. This can be a bit too much trouble for the average user.

This is different from normal applications.

Have you also installed X11?

I recommend using NeoOffice instead...much less trouble while we wait for OO to come into the modern ages 🙂

I've just downloaded Open Office. I've even managed to put the icon on the dock. But the Open office icon inside the Application folder doesn't show the proper Open Office icon, instead, it has a white circle with a line across.

It should change to the correct icon if you logout or restart.

Also, there an OpenOffice.org icon that looks like a white hard drive on the top right desktop that I can't get rid of. What steps should I take every time I've downloaded a new program?

After you drag the application to the Applications folder, eject the disk image (click the triangle to the its right in the Finder sidebar) and drag the disk image file to the trash.

I believe they will, yes. Works for me at least.

Yes they will. I do that a lot. That is the whole point of Open Office / Neooffice.

Dave