One of the obligations that apply on the festival of Purim is Matanot La'evyonim – gifts to the poor. People are generally very vigilant with regard to the Mitzva of Mishlo'ach Manot on Purim, and most of the money spent on this festival goes towards the purchase of Mishlo'ach Manot. It should be noted, however, that Halacha requires that one prioritize Matanot La'evyonim; one should limit his spending on Mishlo'ach Manot and even the Purim meal in order to increase his spending on Matanot La'evyonim. Most of the people to whom we give Mishlo'ach Manot do not need our gifts and can celebrate Purim honorably without these packages. The poor, however, need our assistance to properly celebrate the holiday. This is the primary obligation of Purim, and one should therefore allocate more money to this cause than to the other Mitzvot of Purim.
Strictly speaking, the obligation requires giving one Peruta – a minimal amount – to two people in need (one Peruta to each). However, the Rishonim (Medieval Rabbinic scholars) write that one should give an amount with which the recipient can purchase a modest meal, consisting of bread and a dip. For us, this would mean approximately $5. Thus, to fulfill this obligation, one must donate $10, so that two people in need receive an amount with which they can purchase a modest meal. Women, too, are included in this obligation, and thus a husband must give a minimum amount of $20, to fulfill his and his wife's obligation. Of course, it is laudable to give more than this amount.
Since Matanot La'evyonim constitutes a Halachic obligation, the $10 that one donates for this Mitzva cannot go towards his Ma'aser, the tithing of his earnings. However, if one gives more than $10 for Matanot La'evyonim, the excess amount may, indeed, be counted towards his Ma'aser contributions to charity.
The Mitzva requires giving Matanot La'evyonim on Purim day itself. Somebody who knows a needy family may go to that family and personally hand them the money, and thereby fulfill his obligation. Preferably, the donation should be given anonymously, such as by putting the money in an envelope and anonymously leaving the envelope by the recipient's door. In most communities there are people who collect Matanot La'evyonim donations before Purim and distribute the money to the needy on Purim, which is the preferred method for fulfilling this Mitzva.
Summary: The obligation of Matanot La'evyonim requires that each person donate a minimum sum of $10 to help needy Jews on Purim, or $20 for a married couple. This obligation should receive budgeting priority over Mishlo'ach Manot and the Purim meal. The money must be given to the poor on Purim day itself; generally speaking, this is done by people who collect donations before Purim and distribute the funds to the poor on Purim.