There, they stand in a wide circle, while the overseer stands in the middle. The drawing only took place in a circle, as opposed to the participants standing in straight lines or in some other fashion, lest one suspect that perhaps the official who chose the number should try in advance to quickly decide who the number should end with, so that he could favor a relative or loved one. The hat of one of those in the ranks is removed, in order to mark the starting point of the lottery. (This is another reason why the lottery was held indoors, in the chamber - since it was considered a mark of disrespect to stand in the Temple court without a hat).
A number would be picked and agreed upon, substantially higher than the number of men present. The overseer would then declare that each man present raise a finger. Then, they would count each extended finger (since the Bible forbids the counting of actual people... see Ex. 30:12; for this reason the census was conducted by the half-shekel donation), beginning with he who stands hatless and moving throughout the circle over and over again until reaching the number that had been pre-selected. The priest whom the chosen number falls upon, is he who has won the right to perform the task (some commentators even maintain that the official who chose the number and the one who removed the hat were two separate people, so that there could be absolutely no room for conniving or favoritism; i.e., no foreknowledge of where the number would land).