The Gemara (Kiddushin 34a) explains that women are exempt from positive Mitzvot that are time-bound and are obligated in Mitzvot that are not time-bound. The Shulhan Aruch (O.H. 106:1) writes that prayer is not a time-bound Mitzvah and therefore women are obligated to pray. Although it is true that in its current form prayer is bound by specific times, such as Shaharit only being able to be recited at certain times, the Torah only requires one to simply pray once a day. In other words, on a Biblical level, one must only recite some sort of personal prayer sometime throughout the day and one will have fulfilled one’s obligation. The Sages eventually instituted a standardized text of prayer and the obligation to pray three times a day, at certain times. The Magen Avraham (96:2), citing the Rambam (Tefila 1:1,2), says that women would fulfill this obligation as long as they recited any sort of personal prayer at some point during the day. The Ramban, however, says that the obligation to pray is Rabbinic in origin and therefore women would be exempt.
The practical ramification of this dispute does not involve whether a woman must pray, since the Halacha follows the Rambam, but rather what prayer must be recited. Unlike the Magen Avraham, Rabbi Ovadia Yosef (Yabia Omer vol. VI, § 17) says that when a woman prays, she should specifically recite the established Amida since it incorporates praises, personal requests and thanks to Hashem. Rabbi Ben Zion Abba Shaul (Or Lezion, vol. II, ch. 7, § 25) and Rabbi Pesach Eliyahu Falk (Mahze Eliyahu, § 19:9) write that women may recite any type of personal prayer, but they must do so twice a day. According to this opinion, if a woman is able to recite the Amida, it should be specifically Shaharit and Minha, since Arvit is considered more of a voluntary prayer. If a woman is able to set aside time to recite two prayers a day, it is certainly praiseworthy.
Furthermore, if a woman prays Shaharit, she should ideally also recite the blessings before and after the the Shema as well as the Shema itself. Although the Shema is a time-bound Mitzvah, there is an opinion that the blessings of the Shema should not be recited with Hashem’s Name. Nevertheless, since there is also an aspect of praise in these blessings, a woman may recite them with Hashem’s Name.
Summary: Women are obligated in prayer at least once a day, but should try to pray twice a day if possible. Women should recite the established prayer rather than a personal supplication.