Gemara

2b (R. Shimon ben Gamliel): There are three Terumos (donations) mentioned in this Parshah (donations for the Mishkan) - [silver] for the Adanim (sockets of the Mishkan), of Shekalim, and Terumas ha'Mishkan. "... Va'Yikchu Li Terumah" was for the Adanim, "...Tikchu Es Terumasi" was the Shekalim, and "v'Zos ha'Terumah..." was [other materials needed] for the Mishkan.

R. Avon says, also in this Parshah (Machatzis ha'Shekel) there are three Terumos. "Machatzis ha'Shekel Terumah la'Shem", "Yiten Terumas Hash-m", and "Lases Es Terumas Hash-m."

3b (Mishnah): We do not take securities [for Machatzis ha'Shekel] from Ketanim.

Inference: We do not take a security from Ketanim, but we do demand the Shekel.

This is only if he brought two hairs [of puberty].

We do not take a security even if he brought two hairs.

6a (R. Chilkiyah): "V'He'emadnu Aleinu Mitzvos Lases Shelishis ha'Shekel b'Shanah la'Avodas Beis Elokeinu" teaches that one must divide his Shekel (give it over the course of) three times in the year.

This shows that we do not exert the Tzibur more than three times a year.

Rishonim

Rambam (Hilchos Shekalim 1:7): If a father began giving for his minor son, he gives every year until the child matures and gives for himself.

Mordechai (Megilah 777): We give three halves for Purim because it says three times "Machatzis ha'Shekel" in Parshas Ki Sisa.

Maharil (Hilchos Purim 4): Mahari Segel says that everyone 20 and above must give Machatzis ha'Shekel. This is 34 Halish. The Siman is "veha'Dal Lo Yam'it mi'Machatzis ha'Shekel." (The Gematriya of Dal is 34.)

Bartenura (Shekalim 1:3 DH u'Ketanim): Even if he brought two hairs, and he is less than 20 years [we do not take a security from him].

Tosfos Yom Tov (1:4 DH Kol (2)): The Bartenura holds that the first verse teaches the half-Shekalim given for the Adanim, and the second was to buy Korbanos. This is why he obligates only one from 20 and above, like the verse says. What forced him to say so? The Mishnah says "Ketanim". Presumably, this is until 13 years, like it normally means. The Rambam says so in Perush ha'Mishnayos and the Mishneh Torah, and the Ramban on Chumash says so. The Yerushalmi explicitly says so. If so, the second verse discusses giving for the Adanim. The first, which does not say "from 20 years", was for Korbanos. Perhaps the Bartenura says that the first verse was for the Adanim because it preceded Terumah for Korbanos. However, how can he explain the Yerushalmi?

Machatzis ha'Shekel (on Magen Avraham 694:3): Our Machatzis ha'Shekel commemorates what they used to give for Korbanos in Adar. Perush ha'Mishnayos says that the first verse discusses this, and it does not mention 20 years.

Poskim

Rema (OC 694:1): Some say that one should give before Purim half the fixed coin in that time and place, to commemorate Machatzis ha'Shekel that they used to give in Adar. Since it says "Terumah" three times in the Parshah, one should give three.

Kaf ha'Chayim (23): Even in the time of the Mikdash, they gave only one half-Shekel a year. The other two Terumos mentioned in the Parshah applied only in the year that they built the Mishkan. Why must we commemorate it? The custom to give three did not spread everywhere, rather, just half the smallest coin. Even this is not uniform. Some give more, and some give less, since it is a mere commemoration. This is why Ma'aseh Rav [of the Gra] says that it suffices to give one half gold Polish.

Rema (ibid.): One should give three big halves in these lands, for there is no other coin here called "half". In Austrich one gives three half Vainars, for these are also called half. The same applies to every land.

Darchei Moshe (1): Minhagei Mahara Kloizner says that for Ma'os Purim, in every place that has a fixed coin, we take three halves of that coin, and give them for Ma'os Purim, and not of another coin used elsewhere. In our Minhagim, it says to give three half Vainars. I say that for our coins, it is good to give three big halves, for they are called half a big [coin], just like Machatzis ha'Shekel. Also, Machatzis ha'Shekel was 10 Gera, and half a big coin is nine small coins, and it itself completes 10. Also, there is no other coin here called "half". This is unlike those who give three Chalakim, since Minhagim says to give three half Vainars. This is wrong. In every place, one gauges based on the fixed currency, like I explained above.

Bi'ur Halachah (DH v'Yesh Liten): The custom is to explain that a half big coin is a half-Polish, called a half-Grashin in our lands. Darchei Moshe connotes unlike this. Perhaps there was another coin in his land that was nine small coins. Here we have no such coin. Here, it seems that letter of the law one is Yotzei with a half-Grash, but this is not an important coin at all, even if one gives three, unless he gives also for his minor children. Some Gabayim put three half-rubles in the Tzedakah bowl from the beginning, and when one comes to give, the Gabai gives to him three half-rubles in place of the donor's coins, and the donor puts the three half-rubles in the bowl. This is wrong. If the Gabai merely lends the coins to him for a few moments, and the donor does not intend to give them to Tzedakah, this is not giving at all! He deceives only himself. If the Gabai truly intends that the first donor acquire the coins to him, and he gives them to Tzedakah, this helps for the first donor, but not for later ones. The coins already became Tzedakah, so the Gabai may not exchange them for three half-Polishim. Perhaps because this is the custom, it is as if all who give to Tzedakah explicitly stipulated that the Gabai may do so. In the time of the Gra there was a half gold Polish, and Ma'aseh Rav says that the Gra gave only one half gold Polish. This coin is not found nowadays. One must give three half Grashin, or half a silver ruble. One who is able to give a [whole] silver ruble to commemorate Machatzis ha'Shekel, and three half Grashin due to the three times it says Terumah in the Parshah, like the latter opinion in the Rema, he is fortunate, and it will be good for him.

Kaf ha'Chayim (20): One who is able to should give a coin called half with at least a half-Shekel of pure silver, like the Rambam says about Shekalim that they gave at the time of the Mikdash, which is three Drahams of silver. It says so in Shulchan Aruch (YD 305:1, that the five Sela'im of Pidyon ha'Ben are 30 Drahams. The Shekel ha'Kodesh equals a Sela.) If there is no such coin in his place, either he gives a silver coin with which one can buy three Drahams of silver, or Shavah Kesef (Metaltelim worth this amount). Our commemoration is more stringent than Pidyon ha'Ben, for which it suffices to give coins or Shavah Kesef. One should give silver if possible, to commemorate Machatzis ha'Shekel, which was of silver. If he cannot, it suffices to give a coin called half.

Ashrei ha'Ish (3 42:1, citing ha'Gaon R. Y.S. Elyashiv Ztz"l): In Eretz Yisrael, it is good to give three American half-dollars in addition to three half-Shekels. (Ha'Gaon R. Y.S. Elyashiv would give half-dollars containing actual silver, and then three half-Shekels.) If one in the U.S. cannot get half-dollar coins, he gives any amount of money more than a Perutah.

Rema (ibid.): Only one above 20 is obligated to give.

Darchei Moshe (1): Maharil connotes that only one 20 and above is obligated to give. Minhagim says that even children give. Even though Maharil's opinion is more reasonable, one should not change the custom.

Magen Avraham (3): This is like the Bartenura. The Tosfos Yom Tov wrote that the Poskim disagree, and obligate from 13 years.

Gra (DH v'Ein): This is like it says in the Parshah "mi'Ben Esrim." The Yerushalmi discusses two hairs. After two hairs, one is obligated if he already gave once.

Mishnah Berurah (5): Eliyahu Rabah said that the Bartenura and Tosfos Yom Tov argue about letter of the law. The custom is to give even for one's minors, and a pregnant woman for her fetus.

Ashrei ha'Ish (ibid., 6): If one began giving for women, even though he was not obligated, now it is like a vow to Tzedakah, and he may not cease giving.