In ancient times when the Holy Temple was built, sacrifices were brought to the Holy Temple to atone the sins of the Jewish nation. The Torah states that the money for the sacrifices should come from the entire public, rich and poor, so that everyone will have an equal atonement before Hashem. The Torah also mentions that the sacrifices should be brought every year in the month of Nissan, from a new donation that would be collected close to Nissan. The sages ruled that the donations should be collected in the Month of Adar in order to precede our Shekels (money) to the Shekels Haman gave Achashverosh so that he would be allowed to destroy and obliterate the Jewish nation.
Nowadays, the Holy Temple hasn't yet been rebuild, this donation is not a Mitzvah but a custom to give an amount of money equal to half (Machatzit) a Shekel (a silver biblical coin), as a remembrance (Zecher) to the ancient half Shekel that was given to the Holy Temple. Therefore its name: Zecher LeMachatzit HaShekel – A remembrance of the half Shekel. In fact, both the Rambam and Shulchan Aruch don't mention this custom, only the Rema does, but still this is an ancient Jewish custom, and Sephardi Jews kept this decent custom as well.
Who is obligated to give Machatzit HaShekel?
The original obligation was only for men, some say from the age of 21 and above and some say from the age of 13. Rabbi Binyamin Bamberger mentioned that the Kaf Hachayim (סימן תרצד, אות כז) wrote that even women need to give Zecher LeMachatzit HaShekel since it gives atonement for the soul and even when the Holy Temple was built if a woman wanted to give this donation she was accepted. All the more so when this money goes to charity. Rabbi David Chai Hacohen wrote that even though women are really exempt from this custom, since they haven't sinned in the sin of The Golden Calf and therefore don’t need this atonement, still, there is a custom to give Zacher LeMachatzit HaShekel for women and children as well. Rabbi Avigdor Neventzal added, that giving for children that are less than 13 years old, is indeed a good custom, but there isn’t a real obligation to give.
When should I donate this money?
Most of the people give the Zecher LeMachatzit Hashekel before the Mincha of Ta'anit Esther (the Fast of Esther) or immediately after it, but there's no need to be meticulous about it, and it can be given during the entire month of Adar. In fact, if one hasn’t given it in the month of Adar, he can and should give it during the entire year.
If someone forgot to give the Zecher LeMachatzit HaShekel and remembered just a year later in the month of Adar, Rabbi Yaakov Ariel ruled that in such case there's no need to give it twice. However, Rabbi Azaria Ariel mentioned that there are opinions that say he should fulfill his obligation from the last year and give twice.
Should I say something when I give it?
The custom is to say 'Zecher LeMachatzit HaShekel' when giving the money to charity, and it's important not to say 'Machatzit HaShekel' only (without saying the word "Zecher") so that the money won't be consecrated to the Holy Temple, such money cannot be used for other needs.
Rabbi Dov Lior was asked about a person that said 'This money is for the Machatzit HaShekel that is given in the month of Adar', is this money indeed consecrated to the Holy Temple? Rabbi Lior answered that nowadays, since no one gives the real Machatzit Hashekel but only the Zecher, this person probably didn't really mean to consecrate this money, and this money can be donated to charity.
Who should I give this money to?
Rabbi David Chai HaCohen wrote that today that we don’t have the Holy Temple, it is fitting to give this money to the building of a synagogue, or for its needs such as lighting, etc. because the synagogue is called a "Mikdash Me'at" (a small Temple). In exchange, he offered to give the money for Yeshivot or Torah scholars since the Gemara tells us that " Since the day the Holy Temple was destroyed, the Lord has only one place in His world where he reveals His presence exclusively; only the four cubits where the study of halakha is undertaken".
Can one give Machatzit HaShekel from his Ma'aser Ksafim?
Ma'aser Ksafim should be donated to things you don't have to give, and since Machcatzit HaShekel is custom that we are obligated to keep, Rabbi Dov Lior ruled that one Cannot give the Machatzit HaShekel from his Ma'aser Ksafim.
How much should one give?
The common custom among Ashkenazi Jews is to give at least three coins of half of the local currency (Dollar, Euro, NIS, etc), however, most of the Sephardi Jews give the actual value of the biblical Half Shekel. There is a disagreement on how much does the biblical half Shekel is worth today. Rabbi David Chai HaCohen wrote that the value Is 10 grams of pure silver, Rabbi Dov Lior holds that the value is 8.5 grams of pure silver.
Rabbi Yaakov Ariel added that even for those who give the actual value, there is no need to add the taxes one needs to pay when buying silver, on the other hand, Rabbi Yehuda Amichai ruled that the taxed should be brought into account.
Important to mention, that each person can donate more than the above sum, and so it is appropriate to do.
Needless to mention, the Zecher LeMachatzit Hashekel can be donated to Yeshiva.co, and there is a special advantage in doing so because with a small amount of money you can spread Torah to thousands of people worldwide. You can donate using the secure donation form.