לְשַׁבָּחָא 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. 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 can be divided into three parts, verses 2-7 which praise creation and specifically the sun, verses 8-11 which praise God's Torah and commandments, and verses 12-15, in which the psalmist requests that Hashem guard him from sin. Regarding the relationship between the various parts see the note on verse 8.