One is required to stand out of respect for his father or mother once the parent comes within eyeshot, meaning, within 160 meters, or about 500 feet. If the parent comes within this distance, and the child sees the parent, the child is required to stand as a sign of respect. According to Sephardic custom, this applies each and every time the child sees the parent, even one hundred times a day. Ashkenazim follow a more lenient position, but Sephardic custom follows the stringent view of the Rif, Rashba and Rosh that one must stand out of respect for his parent no matter how many times he sees the parent.
After one stands for his parent, he must remain standing until the parent reaches the place where he or she will be sitting or standing. Once the parent reaches his or her place, the child may sit down. However, there is a custom (noted already by the Hida) that when one’s father (or Rabbi) receives an Aliya to the Torah in the synagogue, the child remains standing until the Aliya is completed and the father returns to his seat and sits down. One who does not observe this custom, and sits down once his father reaches the Sefer Torah, is infringing upon his father’s honor, even though, technically speaking, he has not violated Halacha.
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Parashat Ki-Teseh (15), rules that if one is praying in the synagogue and sees his father enter the room, he must stand, even if he is in the middle of Pesukeh De’zimrah or even the recitation of Shema. Although some Halachic authorities dispute this ruling, the Ben Ish Hai’s view was accepted by Hacham Ovadia Yosef. Likewise, one who is reciting Birkat Ha’mazon and sees his father enter the room must stand.
If one’s parent enters the room while he is learning Torah, he must interrupt his learning in order to stand out of respect. Generally, one who is involved in a Misva is not required to interrupt to perform another Misva that comes his way ("Osek Be’misva Patur Min Ha’misva"). However, this rule does not apply to Torah learning, since the purpose of Torah learning is to lead us to the observance of Misvot, and thus one must interrupt his Torah learning for the performance of a Misva, such as standing for one’s parent.
The obligation to stand for one’s parent applies even on a train or bus; if one’s parent walks onto the train or bus, the child must stand. It goes without saying that if there aren’t enough seats on the train or bus, the child must offer the parent his or her seat.
Summary: One is required to stand when his parent enters the room, from the moment he sees the parent until the parent reaches the spot when he or she will be sitting or standing. When one’s father is called to the Torah in the synagogue, it is customary to remain standing until the father returns to his seat after the Aliya. One must stand when his parent walks into the room even if he is in the middle of praying Pesukeh De’zimra or Shema, or reciting Birkat Ha’mazon.