Parshas Shekalim is read the week before Rosh Chodesh Adar. If Rosh Chodesh falls on Shabbos, it is read on Rosh Chodesh itself. In the times of the Beis Hamikdosh, the call for the collection of shekalim began on Rosh Chodesh Adar. Parshas Parah, which commemorates Klal Yisroel purifying themselves for the Korbon Pesach, is read the week before Parshas Hachodesh. Presently, when purification is not a possibility, the reading serves as a tefillah for the opportunity to purify through the Parah Adumah. Parshas Hachodesh is read the week before Rosh Chodesh Nissan. If Rosh Chodesh falls on Shabbos, it is read on Rosh Chodesh itself. The reading serves as a form of sanctifying the new month of Nissan.
[שו"ע תרפה, א, ג, ד ו־ה, ומשנ"ב א; ביאורים ומוספים דרשו, 3 ו־5]