Answer:
The controlling umpire (the one who awarded the penalty corner and whose circle it is in) should first stand in a central position and make sure both teams are ready; this includes having all necessary players present, that they are all out of the circle, that the ball is in the correct place. When this is so, they should step back to a position from which they can see all possible action and signal that the corner may begin. After this, they should first be watching for two things: was the ball played in legally, and did any players break early? If the umpire is happy no breach of rule occurred, the penalty corner should play. Following this, they should then consider whether any shot taken was legitimate, whether a player commits a foul, whether any action has caused the penalty corner to be over (if relevant) and all other standard aspects of open play.
The secondary umpire should also position themselves so that they can see the whole - or as much of - the goalmouth as possible. This also allows them to see the top of the circle, which is often an important area in a PC. They should check that all players are behind the hafway line where necessary, and signal if there is an advantage gained from this not being so (normally the arm is raised until all players are behind it, or until the advantage is used). They should always be mindful of substitution actions during the PC - a player can go off, but the sub cannot come on until finished. While the PC is played, they should pay attention to the line of any shot: whether it was going in or was too high/low for a particular purpose and whether it was played illegally by any player, as this can sometimes result in a call being made or change. Finally, they should also be watching to ensure the ball left the circle and also that any condition for the substitution or for calling time has been met.