According to the Jewish calendar, the fourteenth of Adar will never fall on a Shabbos. The fifteenth can fall on Shabbos. When Purim falls on Shabbos, it is known as a Purim Meshulash. The schedule is as follows: The Megilah is read on Friday. Matanos L’evyonim is distributed on Friday as well. On Shabbos, one should expound upon the Megilah. Al Hanissim is added to davening and bentching. The Maftir is the kriyah of Purim. The Seudas Purim and Mishloach Manos take place on Sunday. Some distribute Mishloach Manos on Shabbos. They also add a special food to the Shabbos meal as a fulfillment of the Purim Seudah. A third view maintains that the Mishloach Manos should be given out on Friday.
[שו"ע תרפח, ו, משנ"ב יד, טז, יזי ו־יח, ושעה"צ ל; ביאורים ומוספים דרשו, 33 ו־35]