1) THE ANNOUNCEMENT OF THE COLLECTION OF SHEKALIM ON THE FIRST OF ADAR
OPINIONS: The Mishnah states that the announcement of the commencement of the annual collection of Shekalim is made on the first of Adar. However, the Shekalim that are collected are not actually used until the first of Nisan, when the Terumas ha'Lishkah is performed and public Korbanos are purchased with the money. Why is the announcement made thirty days before the Shekalim are needed?
(a) The Gemara in Megilah (29b) derives from the law that "we expound (Sho'alin v'Dorshin) the Halachos of the festival thirty days before the festival" that the period of preparation for an event is thirty days. Accordingly, the announcement of the collection of Shekalim is made thirty days before the public Korbanos will be bought.
The Gemara in Megilah cites another opinion, that of Raban Shimon ben Gamliel, who maintains that we expound the Halachos of the festival only fourteen days (two weeks) before the festival. According to Raban Shimon ben Gamliel, the period of preparation for an event is fourteen days, and not thirty. The Gemara in Megilah explains that according to Raban Shimon ben Gamliel, the announcement was made on the first of Adar because that day is fourteen days before the day on which the collection begins in earnest, the fifteenth of Adar. On the fifteenth of Adar, the moneychangers begin to operate for those who donate their Shekalim.
(b) RABEINU MESHULAM suggests an original explanation. The Gemara in Ta'anis (7a) says that it takes fifteen days to travel from Yerushalayim to the farthest point in Eretz Yisrael. The announcement of the collection of Shekalim is made on the first of Adar in order to inform the people who live throughout Eretz Yisrael that the time for the collection is approaching. (The announcement for those who live outside of Eretz Yisrael is made earlier, according to one opinion in the Gemara.)
Rabeinu Meshulam explains that the Beis Din in Yerushalayim issues the announcement and sends out messengers to inform all of the towns in Eretz Yisrael. It takes them fifteen days to reach the farthest places in Eretz Yisrael, and it takes another fifteen days for the Shekalim to arrive in Yerushalayim from those places. Therefore, the announcement is made on the first day of Adar. The Gemara in Megilah (ibid.), which gives a different reason for why the announcement is made on the first of Adar, perhaps maintains that it is not necessary for the Shekalim to arrive in Yerushalayim by the first of Nisan; they may arrive later than the first of Nisan (in accordance with the other opinion quoted here, later on the page). The Gemara here argues and maintains that all of the Shekalim must be collected by the first of Nisan, and that is why the announcement is made on the first of Adar.
(c) The Gemara earlier in Megilah (end of 13b) gives another reason for why the announcement of the Shekalim is made at the beginning of Adar. The Gemara says that Hash-m commanded the Jewish people in the desert to give a half-Shekel, because Hash-m knew that many generations later the wicked Haman would give a large sum of Shekalim to Achashverosh in exchange for the right to destroy the Jews. The sum of Shekalim that Haman would give would correspond to the total amount of Shekalim that the Jews gave when they were first commanded to give Shekalim in the desert. By commanding them to give Shekalim, Hash-m "prepared the cure before the illness," for in the merit of their Shekalim, the Shekalim of Haman were ineffective. Therefore, the Rabanan enacted that each year, the announcement to give the half-Shekel should be made before the time of Haman's lots (which were drawn on the thirteenth of Adar).
Why, though, did the Rabanan enact that the announcement be made two weeks before that time? The VILNA GA'ON (in MISHNAS ELIYAHU) explains that according to the Midrash, Haman rejoiced that his lots chose the month of Adar, the Mazal of which is Dagim (Pisces). Haman viewed this as an ominous omen for the Jews, because fish swallow each other. To counteract the potentially inauspicious Mazal of Adar, the collection of Shekalim starts at the beginning of the month. The Mitzvah of Shekalim arouses Hash-m's mercy to transform the potential of the Mazal of Adar into an auspicious one for the Jewish people (so that their enemies should be swallowed up like fish). 2b----------------------------------2b
2) PUBLICIZING THE TERUMAS HA'LISHKAH
OPINIONS: The Gemara quotes the Mishnah later (3:1) which states that the Terumas ha'Lishkah is done at three different times during the year. The Gemara concludes that the reason the Terumas ha'Lishkah is done at three different times, and not all at one time, is not because the money arrived from different places at different times. Rather, it is done to publicize the event of the Terumas ha'Lishkah. What is the purpose of publicizing the Terumas ha'Lishkah?
(a) RABEINU MESHULAM explains that the Terumas ha'Lishkah is publicized in order to show the people what the Kohanim do on behalf of the Tzibur with the Shekalim that they sent, so that the people should not think that they sent Shekalim for nothing.
(b) The TALMID SHEL RABEINU SHMUEL BAR SHNEUR and the TIKLIN CHADTIN explain that the three times at which the Terumas ha'Lishkah is done are times of Aliyah l'Regel -- when the people who live far away come up to Yerushalayim. The Chachamim enacted that the Terumas ha'Lishkah be publicized to those people to demonstrate to them that their Shekalim are being used for the public Korbanos.
(c) The RAMBAM (Perush ha'Mishnayos 3:1) explains that although the Terumah at the beginning of the year is done on behalf of all of the Shekalim that were collected and that will be collected that year ("Al ha'Asid li'Gevos"), and thus it is done for all of the Jewish people, the Shekalim from the places that are far away do not actually arrive at the Beis ha'Mikdash until later. The Shekalim sent by the people who live closer to Eretz Yisrael arrive by Shavuos, and the Shekalim of those who live far away from Eretz Yisrael arrive by Sukos.
The Chachamim instituted that the Terumas ha'Lishkah be performed at each of these times in order to remind the people from outside of Eretz Yisrael that by this time their Shekalim must arrive. Since the people know that this public act will be done at that time in Yerushalayim, they are careful to send their money early enough in order for it to arrive by that time.

OTHER D.A.F. RESOURCES
ON THIS DAF