The hand pass or handball is probably the one thing that most obviously distinguishes Aussie Rules from most other ball sports you might have seen.  It is a pretty simple thing to describe, but quite difficult to actually do under pressure and many new players get penalised by the umpires for throwing during a match.

It is also the skill which can really get you out of a fix, with a hand pass often being the quickest and easiest way of getting the ball out of trouble before a crunching tackle.

Cradle the ball in your non-striking hand but don't grip it too hard.  Make a fist with your striking hand, making sure that the thumb is on the outside - you are aiming to hit the ball on the point with the V shape made by your index finger.  Bring your striking arm back and at the same time step forward in the same direction as you want the ball to travel.  Bring your striking hand forward and hit the point of the ball, sending it spinning backwards to your teammate.  It's a good idea to get into the habit of catching your striking hand with your non-striking hand to get the technique right.

Of course this all presumes you have the time to make this perfect hand pass, more often than not you will be under pressure and falling over, but if you manage to get the proper technique right you will be able to adapt it for whatever situation or angle you find yourself in. 

Remember that you are not allowed under any circumstances during a match to throw the ball - if you do, whether you meant to or not, you will concede a freekick.  Umpires might give EUs a bit of leeway every now and then but don't rely on it!