My iPad is stuck in the vertical orientation, I can't get it to change to horizontal, how do I fix that?

Is there a lock symbol at the top of the screen next to the battery indicator ? If there is, then depending on what you've got Settings > General > Use Side Switch To set to (rotation lock or mute notifications), then you can lock/unlock the rotation by the switch on the right hand side of the iPad above the volume switch, or via the taskbar : double-click the home button; slide from the left; and it's the icon far left; press home again to exit the taskbar. The function that isn't on the side switch is set via the taskbar instead : http://support.apple.com/kb/HT4085

If there isn't a lock symbol then try a reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.