You wrote to ask whether women have the same obligation in daily prayer as men according to Judaism. This is actually a more complex question than it might seem, because there is disagreement among authorities how to understand anyone’s obligation for daily prayer.
Jewish law obligations are divided broadly between those that have the authority of the Torah (biblical commandments) and those that have the authority of later enactment by the rabbis (rabbinic commandments). Understanding this is key to understanding the debate that unfolds about women’s prayer.
Maimonides leads a group of early authorities who think that there is a biblical obligation for all Jews to pray to God at least once a day, in whatever language or format and at whatever time they choose (See his Hilkhot Tefillah 1:1-2). According to the Torah, in other words, a person can pray in whatever manner they choose, though their prayers should include words of praise, request and thanks. This obligation applies to both men and women equally. However, the later rabbis, according to Maimonides, added specifications. For men, they specified a fixed, Hebrew liturgy (preserved in the traditional prayer book) as well as fixed times for prayer in the morning, afternoon and evening. Thus, the rabbinic obligation to pray is a “time bound positive commandment” from which women are typically exempt. This is the approach adopted by Rabbi Joseph Caro’s Shulchan Arukh (Orah Hayyim 106:1), according to which women need to pray once a day in whatever language they choose, whereas men must pray three times a day from a fixed liturgy. There are many contemporary women who follow this view.
There was however also a completely different view of prayer articulated by another group of early authorities, including Nahmanides, Rashi and others. They argued that there is no biblical commandment to pray every day (though when you do pray there is a commandment to pray only to God) but only a rabbinic one. Some authorities who held to this view felt that women’s exemption from time-bound, positive commandments does not apply at all to rabbinic enactments and that women should therefore be obligated in daily prayer just like men. Others held that the exemption does apply to rabbinic enactments, but that prayer is exceptional because of the sheer importance of begging God for mercy. In this latter view, women are obligated to pray each day from the fixed liturgy, though not exactly in the same way as men are. They may, for instance, only be obligated once or possibly twice a day—both customs that are also well represented among contemporary women (See Arukh Ha-Shulchan OH 106:7).
I am sure that this is more detail than you sought when you asked the question, but it is important to understand that there are many different practices in this area of Jewish law and that this stems to some extent from a legitimate diversity of opinion among scholars. Some women pray at home in their own language, others follow the set liturgy once or twice (more rarely three times) a day and some make a point of attending daily public services. Sometimes, women have also gathered to pray together separately from men, as many do today in all-female school settings. It is wise to consult the custom and halakhic authority of your own community.
Chava Weissler’s book Voices of the Matriarchs (Beacon Press, 1998) contains an excellent historical account of vernacular Yiddish prayers or techines that were composed by East European Jewish women for different occasions and some of these have also recently been translated into English.
You asked about legal obligations but at the end of the day, prayer is also about finding ways to draw close to our creator, our community, and our heritage. Cultivating a prayerful life is a fundamental challenge in our society no matter what your gender, and I wish you every blessing and success in doing so.