The shofar must be blown during the day, as the verse states, “In the seventh month, on the first day of the month…you shall observe it as a day of blasts” (Bamidbar 29:1). Therefore, the time to fulfill the mitzva begins at sunrise. If one blows it from the time of dawn (when the first light is visible in the east), he fulfills his obligation. If he did not blow the shofar before sunset, he should do so during twilight (bein ha-shmashot), but without a berakha (Megilla 20b; SA 588:1; MB ad loc. 1-2; for more about these times, see Peninei Halakha: Prayer 11:1 and Peninei Halakha: Shabbat 3:1).
As we have seen (section 3), the Sages instituted that the communal shofar-blowing take place during Musaf. The poskim write that if one is unable to pray with a congregation, and so is unable to blow the shofar during Musaf, he should blow the shofar after the first three hours of the day, as judgment is more benign later in the day (Mateh Ephraim; MB 588:2; 3:10 above).
Men are obligated in the mitzva; women are exempt since it is a time-bound positive mitzva. Women who nevertheless wish to hear the shofar fulfill a mitzva and will be rewarded for it. The custom of most women is to voluntarily fulfill this mitzva. The Rishonim disagree as to whether women hearing the shofar should make a berakha (Peninei Halakha: Women’s Prayer 2:8, 23:2). Some say that the berakha was instituted only for men, who are obligated in the mitzva, but a woman who blows the shofar for herself should not recite a berakha. Similarly, if a man blows the shofar for women, he should not recite the berakha. This is the Sephardic practice. Others say that even though women are exempt from the mitzva, those who choose to hear the shofar should make a berakha because they are indeed fulfilling a mitzva. Thus, if a woman blows the shofar for herself, she recites a berakha, and if a man blows the shofar for women, one of them should recite the berakha on behalf of all the women present. This is the Ashkenazic practice.
There is a mitzva to train a child who has reached an educable age – that is, a child who can understand that there is a mitzva to hear three sets of tashrat, tashat, tarat – to hear the shofar. If he is too young to understand this, there is no mitzva to train him. Nevertheless, as long as a child can stand quietly and not disturb the worshippers, it is good to bring him to hear the shofar. It is an opportunity for children to gain memories of the holy atmosphere. However, a child who has trouble sitting quietly during teki’ot or prayer and is likely to disturb other worshippers may not be brought to services (MB 587:16).
After fulfilling the mitzva to hear the shofar, blowing it unnecessarily is prohibited, as it is considered a weekday activity, like playing a musical instrument. However, the prohibition does not apply to children. On the contrary, children who are of an educable age should be encouraged to blow the shofar all day long, so that by the time they reach halakhic maturity (at the age of bar or bat mitzva), they will know how to do it (Rema 596:1). Nevertheless, they must be careful not to blow the shofar while people are sleeping.