לְשַׁבָּחָא בִּנְגִינָתָא עַל כִּנָרָא דִתְמַנְיָא נֵימַיָא תּוּשְׁבַּחְתָּא לְדָוִד.
1. For the conductor | לַמְנַצֵּחַ – See Rashi and Ibn Ezra on Tehillim 4:1 that the verb "לנצח" means to supervise, as per its usage in Ezra 3:8 and Divrei HaYamim II 2:1. As such, the term "מְנַצֵּחַ" might refer to a musical director. Cf. R. Saadia (cited by Ibn Ezra there) that the word is connected to the noun "נצח", eternity, and that the title implies that David established the psalm to be sung or played perpetually.
2. to be accompanied by music | בִּנְגִינוֹת – See Ibn Ezra on Tehillim 4:1 that "נְגִינוֹת" might refer to a melody (with the plural form indicating that the hymn was to be played to two tunes) or to an instrument which was so called.
3. on the Sheminit | עַל הַשְּׁמִינִית – The meaning of this word is debated. It might relate to the number "שְׁמֹנֶה" (eight) and refer to an instrument with eight holes or strings (Rashi, R"Y Kara). Alternatively, it might refer to a specific tune, perhaps the eighth of a known list (Ibn Ezra), or be a technical term referring to a certain pitch or span of notes, like the word "octave".
4. of David | לְדָוִד – Many psalms include "לְדָוִד" in their title. See Ibn Ezra and Radak in their introductions to the book, that the term means that the psalm was composed either by David, about David, or in honor of David. This psalm appears to be a request that Hashem save the author from some dire sickness (Rashi, Radak). However, the mention of enemies in verses 8-11 leads others to suggest that the plea to be cured is a metaphoric way of requesting salvation from foes. It is also possible that the author is beset by two dangers at once (Malbim), or that the poet refers to some other unknown source of distress which caused his enemies to rejoice.