Yoma, Chapter 2, Mishnah 1. At the end of the previous chapter we discussed the mitzvah of terumas hadeshen (the removal of the ashes), and the fact that on Yom Kippur it was performed very early, at midnight. Our Mishnah adds further details and explains how terumas hadeshen was performed on an ordinary day.
"Barishonah kol mi sherotzeh litrom es hamizbe'ach torem":
At an earlier stage in history, any kohen who wished to perform terumas hadeshen was able to do so. It is worth noting that whether terumas hadeshen on Yom Kippur had to be done specifically by the Kohen Gadol is a matter of discussion; our Mishnah is dealing with the procedure as it took place on a regular basis.
The race up the ramp:
"Mizman shehein merubin" - when there were many kohanim who wanted to perform terumas hadeshen.
"Ratzin ve'olin bakevesh" - they would hold a race up the ramp leading to the Altar.
"Vechol hakodem b'arba amos zachah" - the top four amos of the ramp, closest to the Altar, are the finish line, and whoever reaches them first wins the right to perform terumas hadeshen.
"Vehayu shneihem shavin":
If two kohanim arrived together - and of course, they had no precise means of deciding the matter, only an estimate - "hamemuneh omer lahem: hatzbi'u". The memuneh, the kohen who was in charge of the service, would tell them to put out their fingers, so that the fingers could be counted and a lottery conducted on that basis.
The reason the lottery was conducted by means of the fingers is that it is forbidden to count Jews, and therefore they count fingers rather than people.
How the lottery was conducted:
The kohanim would stand in a circle and stretch out their fingers. The memuneh would choose a number - higher than the number of people standing there - remove the turban of one of the kohanim to mark where the counting would begin, and count the fingers around the circle. The kohen on whom the number ended was the one who won the right to perform the service.
"Umah hein motzi'in? Achas o shtayim":
Since the counting is done with fingers, the Mishnah specifies how many fingers a person puts out: one finger or two fingers. A healthy, strong person puts out one finger, while a weak person who can only put out two at once puts out two, and they are counted as one, since it is evident that they belong to a single hand.
"Ein motzi'in hagudal bamikdash":
A kohen may not put out his thumb in the Mikdash. The reason: since a large gap can be opened between the thumb and the finger next to it, it would appear to the kohen counting around the circle as though these were two different people, and the finger and the thumb would be counted as two separate counts. They were concerned that a clever kohen would figure out which number was going to come up, and upon seeing that the count was approaching him, would put out an additional finger in order to ensure that the lot would fall on him or on his friend. For this reason they said that one does not put out the thumb in the Mikdash.
In summary: In this Mishnah we learned about the development of the procedure for winning the right to perform terumas hadeshen: originally, anyone who wanted it received it; once there were many who wanted it, the matter was decided by a race up the ramp, with the top four amos serving as the finish line. If two arrived together, the memuneh conducts a lottery by having them put out their fingers, since we do not count Jews but rather their fingers. One puts out one finger or two (which are counted as one), and one does not put out the thumb, out of concern that it would be counted as two people and would make it possible to manipulate the lottery.