Are you new to iOS? If so, welcome! Things work a bit differently on iOS than on OS X. Are you using OS X 10.7 or later on your Mac? If so, think of iOS apps as operating in the "full screen" mode of OS X applications (activated on OS X by clicking the right-most, double-arrow icon on the top of a program window, for applications that support it). You don't minimize applications, you just go between them.
Unlike OS X, an application that doesn't have focus is "paused" in the background. In other words, it will not continue to do active work, but it will be in the same state when you return to it (unless the application is closed completely, and isn't programmed to resume from where you left off). Additionally, many applications do not need to be opened in order to receive data. I don't use Skype, but you can receive FaceTime requests even if you haven't launched the FaceTime app, yourself.
If you want to more easily switch between applications, you can do a quick double-tap of the Home button to bring up the "task manager." Since you're using an iPad, you can also use a gesture that is unavailable to iPhones: swipe upward on the screen with
four fingers (I find it easiest to do this with all fingers excluding the thumb). This will show you your most recently-used applications, and as of iOS 8, your most recent contacts above them. You can scroll side-to-side across the applications, and tap on the one that you want to bring into focus. Be aware that swiping upward on one of the window previews will forcefully quit the application - a useful thing to do if an app is badly misbehaving (which is rare), but also something to be aware of so that you do not perform it by accident.
Lastly, since you asked about FaceTime and Skype, be aware that FaceTime works the same on iOS as it does when in fullscreen mode on OS X. If you're in a FaceTime video call with someone, pressing on the home button (or looking at anything besides FaceTime) will pause the video, but will keep the audio running. So it isn't quite so easy to multitask (or pretend that you're listening and watching... while really doing something else
). I can't speak for Skype, but I wouldn't be surprised if it were similar.
