Simply put, the field umpires have full control the game and start/restart the game, award free kicks or 'dish out' penalties. They may, in their discretion, overrule a decision made by a boundary or goal umpire.

Each field umpire controls roughly one third of the ground. The umpire in the third where the ball is currently being disputed is the umpire in charge at any one time, but any field umpire may bring attention to infringements of the rules that occur 'behind the play'.

Boundary umpires

Boundary umpires (as their name suggests) umpire the boundary lines. They decide if a ball is "out" or if it is "out on the full". They also detect players who enter the centre square illegally and return the football to the centre square after a goal has been scored.

The boundary umpires patrol one side of the ground each.

Goal umpires

The role of the Goal umpire is to decide whether any kick for goal goes between the 2 goals posts (a goal), between a goal post and a point post (a point), has been touched on the way through (a point) or is out on the full (no score).

The field umpire can overrule the decision of the goal umpire and must give the all-clear to the goal umpire before the score is recorded.

The two goal umpires signal and record all scores in a match and compare scores at the end of each quarter to ensure they have the same score.

Two flags are waved to indicate a goal, and one flag is used to indicate a behind. The goal umpire also indicates to the field umpire what the score is by indicating with one finger for a behind and two fingers (one out-stretched on each hand) for a goal.

Emergency umpire

The emergency umpire is not usually actively involved in the game. Their main roles during the game are if a player is sent off for the "blood rule", they escort the player off to ensure there is no time-wasting and they can also report player(s) if they see a reportable offence.

Signals and stuff ...

Who he is ... field umpire
What he does ... taps his left shoulder with his right hand
What he means ... Too high. It is illegal to tackle someone higher than (and including around) the neck.

Who he is ... boundary umpire
What he does ... holds his arms out at right angles to his body and blows the whistle. Will then generally point to the spot where the ball went out.
What he means ... Out on the full. This is when the ball has been kicked over the boundary line without bouncing.

Who he is ... goal umpire
What he does ... holds his left arm in the air and taps his left hand with his right hand..
What he means ... Touched. The kick for goal was touched by an opposition player before crossing the line -- opposition players generally try to touch the ball on the way through so that only one point is awarded ... not 6 points as is the case with a goal.

Who he is ... field umpire
What he does ... crosses his arms across his chest
What he means ... Ball up. Signalled if the ball is buried under a pack of players, but no free is awardable. The umpire will then bounce the ball to restart the game.

Who he is ... goal umpire
What he does ... taps his left shoulder with his right hand
What he means ... Point. The kick for goal has gone been between a goal post and a point post.

Who he is ... field umpire
What he does ... starting with his arms crossed across his chest, he sweeps them out (left arm going left, right arm going right, obviously) to a full sweep.
What he means ... Holding the ball. If the player with the ball is tackled when he still has the ball, he is deemed to be "holding the ball" ... the catch here is that he had to have had a chance to get rid of the ball (ie handball or kick).

Other sources of information