Why do we say Al Naharos Bavel/Shir HaMaalos? Why do few people still say Al Naharos Bavel? Which Poskim/Gedolim did or didn’t say it? Where did the paragraph of Tehillas come from? Which Poskim/Gedolim did or didn’t say it? When do we say Shir HaMaalos as opposed to Al Naharos?
The minhag to say Al Naharos Bavel is brought is brought in the Mishna Brura Siman 1 s”k 11. The purpose of this minhag and of Shir Hamaalos is to remember the churban Bais Hamikdash.
There are varying customs with regards to Al Naharos. Some only say it on Shabbos Chazon. The Mishna Brura write that the main point is to say it with intent and understanding.. Many who feel unable to do so, often do not say it at all.
Shir Hamalos is said at any time there is no tachanun. This includes Shabbos and Yom Tov. Also Erev Shabbos after chatzos [M”B 263:1]. This includes Erev Yom Tov as well [Shu”t Ber Moshe 8:1]. In addition at any seudas mitvah Shir Hamalos is said [Shu”t Hisorerus Hateshuvah 88 s”k 2].