Can I print magazine articles from newsstand?

I suppose it might depend on the publication, but typically no, you can't.

I have never been able to find a way. There is no access to the print dialoge or share options in a magazine. I suppose you could screen capture and then print that but you can't print directly from the magazine.

Hold the home button down and then press and release the power button. The screen will flash when you got a capture.

Presuming it doesn't get locked out, taking the screen cap and then printing that through the photos app is the only way. magazines want to protect their copyright, and allowing you to reprint them without compensation kinda goes against that, so there's no support for printing. Just like there's no support to share movies or share music purchased via iTUnes.

It may have been disabled.

You need to hold down the two keys at the same time, which will take the snapshot. Then you can find the snapshot in your photo app.