שִׁירָא דְאִתְאֲמַר עַל מַסוּקִין דִתְהוֹמָא חֲדֵיתִי בְּאָמְרִין לִי בֵּית מַקְדְשָׁא דַייָ נֵיזֵיל.
1. A song of ascents | שִׁיר הַמַּעֲלוֹת – Regarding the meaning of this title, see the note on Tehillim 120:1.
2. Of David | לְדָוִד – As the psalm revolves around pilgrimage to the Mikdash (the "House of Hashem") which was not yet built in the time of David, this heading might not mean that David composed the psalm, but rather that it was written in his honor. Cf. Ibn Ezra that David wrote it to be said when the Temple was to be built. See also the commentary attributed to Rashbam that even in the time of David, people made pilgrimages to Jerusalem, and that "the House of Hashem" might refer to the site designated as such by David (Divrei HaYamim I 22:1) Finally, see Meiri that maybe after Natan initially responded positively to David's desire to build the Mikdash (Shemuel II 7:1-3), David wrote verses 1-5 in anticipation. When Natan then told him that only his son would build it, he added verses 6-9, a prayer for the city.
3. in those that said to me | בְּאֹמְרִים לִי – See this usage of the preposition "ב" in Shofetim 9:19 or Tehillim 33:21 or 40:17. Alternatively, the phrase might mean: "when they said to me" (as if written: "בשעה שהיו אומרים לי") or: "because they said to me" (Hoil Moshe, pointing to similar usage of the preposition in Bereshit 29:20),