Hello - how do I have more than one app window open at a time on OS X 10.9.1

Just open them and they should all be open on your screen. If you are using the useless "Full Screen" mode, then you will only see one at a time.

You may also have them open on different desktops via Mission Control. http://support.apple.com/kb/HT4689

If that is the case and you don't want them like that, drag them all into one Desktop and remove the rest of them.

You must have put it into full-window mode ( whcih i have never used and never want to either)..I'd search through the system preferneces, find it, and turn it off.

Grant

Well then you are going to have to explain more of what you are seeing. There used to be a "single-app mode" hidden away, but I'm not sure if that is what you are seeing. If it is activated, background apps are automatically hidden.

Do you have any Finder enhnacements installed?

Based on your screen shots, your background apps are not hidden, so did you review the Mission Control basics that I linked to earlier.

It would appear all of your apps are in separate Desktops, which might become apparent if you activate Mission Control (F9, or possibly a function key that looks like three rectangles).

If you do not have Mission Control set up to have each app on a separate Desktop, I have no idea what is causing what you see.