My first iOS device was an iPod touch 1st generation. It was a great device even though when I got it they were already several models old. I got a good deal on it and I was very happy with it except for one thing: that year iOS 4 came out and 1st gens could not upgrade. Now this was actually a good thing, as anyone who has used a 2nd gen on iOS 4 could tell you, if it made the 2nd gen that slow and clunky what would it have done to a 1st gen?
And while it was a good thing in hindsight it made me sad at the time because I missed out on one key new feature: multitasking by double clicking the home button. Multitasking on an iOS device gives you the ability to quickly switch between multiple apps without returning to the home screen each time. It is great for people who want to be more productive by shaving seconds off their work flow, because seconds add up over time.
This concept of shaving time of your work is also what is behind hand gestures on the iPad. I am often amazed at how many people don't know how to use hand gestures or don't make use of them. Hand gestures in many ways are the touch screen equivelent to keyboard commands on a computer.
Make sure they are turned on
Go to Settings > General > Multitasking Gestures, make sure the switch is turned to green (on). You may want to turn these off for some apps (like running games or drawing apps).
1 Finger swiped down from the top of the screen
Brings down Notification center. This works on iPads, iPhones, and iPod touches running at least iOS 5.
1 Finger swiped up from the bottom of the screen
Brings up Control Center. This works on iPads, iPhones, and iPod touches running iOS 7.
1 Finger swiped right from the left side of the screen
Will do different things depending on the app. It may take you back one screen (like in iQtell) or it may pull out a menu (like in Google+). This works on iPads, iPhones, and iPod touches running iOS 7. Some apps also have features when you pull from the right of the screen (like FaceBook) but that is less common.
1 Finger swiped down on the home screen
Opens up spotlight in iOS 7.
2 Fingers pinched in or spread out
Usually controls zooming in an app. This works on iPads, iPhones, and iPod touches.
4 Fingers swiped up from the bottom of the screen
Opens up multitasking (hurray!) on iPads.
4 Fingers swiped left or right from the edge of the screen
Switchs between open apps without using multitasking on iPads.
5 Fingers pinched together
Takes you to the home screen on iPads.
Well those are the ones I know of, if you know of others please let me know :) I hope these help you. And remember, live better.