ת"ר נאמר (שמות כ, יב) כבד את אביך ואת אמך ונאמר (משלי ג, ט) כבד את יקוק מהונך השוה הכתוב כבוד אב ואם לכבוד המקום
The Sages taught that it is stated: “Honor your father and your mother” (Exodus 20:11), and it is stated: “Honor God with your wealth” (Proverbs 3:9). The Torah equates the honour of one’s father and mother to the honour of God.
This is also logical, as the three of them are partners in their creation. As the Sages taught: There are three partners in a person: The Holy Blessed One and their father and his mother. When a person honours their father and mother, the Holy Blessed One says: I'll treat them as if I dwelt among them and they honour Me.
From the roots of this commandment is that it is fitting for a person to acknowledge and return kindness to people who were good to them, and not to be an ungrateful scoundrel, because that is a bad and repulsive attribute before God and people. And they should take to heart that the father and the mother are the cause of their being in the world; and hence it is truly fitting to honour them in every way and give every benefit he can to them, because they brought them to the world, and worked hard for them when they were little. And once they fixe this idea in their soul, they will move up from it to recognize the good of God, Blessed be God, who is their cause and the cause of all their ancestors until the first Adam, and that God took them out into the world's air, and fulfilled their needs every day, and made their body strong and able to stand, and gave them a mind that knows and learns - for without the mind that God granted him, they would be like a horse or a mule who does not understand.
The Sages raised a dilemma before Rav Ulla: How far does the mitzva of honouring one’s father and mother go? Rav Ulla said to them: Go and see what one gentile did in Ashkelon, and his name was Dama ben Netina. Once the Sages sought to purchase merchandise [perakmatya] from him for six hundred thousand gold dinars’ profit, but the key for the container in which the merchandise was kept was placed under his father’s head, and he was sleeping at the time. And he would not disturb him.
Rav Yehuda says that Shmuel says: They asked Rabbi Eliezer: How far does the mitzva of honouring one’s father and mother go? Rabbi Eliezer said to them: Go and see what one gentile did for his father in Ashkelon, his name was Dama ben Netina. Once the Sages wished to purchase precious stones from him for the ephod of the High Priest for six hundred thousand gold dinars’ profit (Rav Kahana taught that it was eight hundred thousand gold dinars’ profit). But the key to the chest holding the jewels was placed under his father’s head, and he would not disturb him.
The next year the Holy One, Blessed be He, gave Dama ben Netina his reward, as a red heifer was born in his herd, and the Jews needed it. When the Sages of Israel came to him he said to them: I know, concerning you, that if I were to ask for all the money in the world you would give it to me. But I ask only that money that I lost due to honouring Dad.
When Rav Dimi came from Eretz Yisrael to Babylonia, he said: Once Dama ben Netina was wearing a fine cloak [sirkon] of gold, and was sitting among the nobles of Rome. And his mother came to him and tore his garment from him and smacked him on the head and spat in his face, and yet he did not embarrass her.
If one's father or mother has become mentally disordered, he should make an effort to behave toward them according to their state of mind until they will be shown mercy. But if he is unable to endure the strain any longer, because they have become utterly insane, he may leave them and go elsewhere, charging others to take proper care of them.
סימן רמ - כיבוד אב ואם בדיבור ג ראה את אביו או אמו שהם בצער ודאגה, ידבר על לבם דברי ריצוי ופיוס להרגיעם ולשמחם, כדי ליישב דעתם. ויש לו לבן ליזהר שלא לספר להוריו דברים שיצערו אותם, אלא אם כן יש צורך שידעו מהדבר. [ילקו''י כיבוד או''א פ''ג ס''ג מהדורת תשס''א כרך א' עמוד רלט]
If a child sees their parents in pain and filled with worry, they should try to jump in and say words to comfort them. This will cheer them up so that they can get their mind off of what’s bothering them. They should be careful not to tell them things that will cause them pain but if it’s something you think they need to know, then tell them.
ח אין לבן להזכיר לאביו ולאמו הטובות שעשה עמהם. [ילקו''י כיבוד או''א פרק ג' ס''ח
A child should not remind their parents of the nice or good deeds they did for them.
סימן רמ - מכבדו בחייו ובמותו
א חייב אדם לכבד את אביו ואמו גם אחרי מותם, ויש אומרים דאין חיוב זה אלא מדרבנן, ויש אומרים שגם לאחר מיתה חיוב כיבוד אב ואם הוא מן התורה. וכן עיקר.
ב עיקר הכבוד הוא לאחר מיתה לרומם כבוד אביו, כגון לקרותו אבא מארי, וכדומה, ולעשות לו נחת רוח לאחר פטירתו, באמירת קדיש, הדלקת נר נשמה ביום הפטירה, [ראה להלן הלכות אבלות, ובילקו''י אבלות סימן מ, ובילקו''י כיבוד אב ואם פרק יג ס''ז], ועריכת אזכרה ביום השנה, עלייה לתורה ביום השנה, וכיו''ב. [ילקו''י כיבוד או''א מהדורת תשס''א כרך ב' עמוד שמא]
According to rabbis, it is a mitzvah to respect your parents even after they passed away. Some say, that this mitzvah even comes from the Torah.
Ways you can respect them: saying kaddish, lighting the candles on shabbat in their memory on the day they passed, making a remembrance every year on the day of their passing, going up to the Torah once a year, visiting their grave.