This psalm consists properly of three parts:
I. A complaint as of one who was forsaken by God; who was persecuted, and who saw no means of deliverance; who took counsel with his own heart how he might be delivered, but who found no way in which it could be done, Psalm 13:1-2.
II. An earnest prayer to God that He would interpose; that He would attend to the cry of the sufferer; that He would enlighten his mind; that his enemy might not be allowed to prevail against him, and rejoice over his fall, Psalm 13:2-3.
III. A cheerful confidence in God that he would grant this favor, and interpose in his behalf, Psalm 13:5-6.
This is entitled, "A Psalm of David," and there is no reason to suppose that he was not the author. Yet there are in it no indications of the time when it was written or of the circumstances under which it was posed. It would seem to have been time of persecution, and it would be most natural to refer its composition to the persecutions which David experienced from Saul. Most of the rabbinical writers understand it as referring to the whole Hebrew people, and as expressing their sentiments and feelings in times of persecution in general. Kimchi understands it as referring to the present exile and trials of the Jewish people. DeWette. The psalm, though undoubtedly composed with reference to the special circumstances and trials of the author, contains sentiments applicable at all times to believers, and may be regarded as exemplifying the way in which pious feeling expresses itself in times of persecution and trial. Individuals are not unfrequently in circumstances in which the language of this psalm exactly expresses the feelings of their hearts; and the psalm is of great and permanent value, therefore, in the church, as illustrating the fact that good people may sometimes feel desolate and forsaken, as if even God had left them; the fact that they will, in such circumstances, cry earnestly to God for his interposition; and the fact that they will have, and will manifest, as the result of such an appeal to God, a cheerful confidence in His protecting care.
The title - "To the chief Musician" (margin, overseer) - is the same as that prefixed to the fourth Psalm, with the omission of the words "On Neginoth." See the notes at that title.

This Psalm contains the sentiments of an afflicted soul that earnestly desires succor from the Lord. The psalmist complains of delay, Psalm 13:1-3; prays for light and comfort, because he finds himself on the brink of death, Psalm 13:3; dreads the revilings of his enemies, Psalm 13:4; anticipates a favorable answer, and promises thanksgiving, Psalm 13:5, Psalm 13:6.
There is nothing particular in the inscription. The Psalm is supposed to have been written during the captivity, and to contain the prayers and supplications of the distressed Israelites, worn out with their long and oppressive bondage.

INTRODUCTION TO PSALM 13
To the chief Musician, a Psalm of David. According to Theodoret this psalm was written by David, not when he fled from Saul, but from Absalom; and gives this reason for it, what happened to him from Saul was before his sin, and therefore he could speak with great boldness; but what befell him from Absalom was after it, and therefore mourning and groans were mixed with his words.

The psalmist complains that God had long withdrawn. He earnestly prays for comfort. He assures himself of an answer of peace.

Suppliant Cry of One Who Is Utterly Undone
The ירוּם of the personal cry with which David opens Psalm 13:1-6 harmonizes with כּרם of the general lament which he introduces into Psalm 12:1-8; and for this reason the collector has coupled these two Psalm together. Hitzig assigns Psalm 13:1-6 to the time when Saul posted watchers to hunt David from place to place, and when, having been long and unceasingly persecuted, David dared to cherish a hope of escaping death only by indefatigable vigilance and endurance. Perhaps this view is correct. The Psalm consists of three strophes, or if it be preferred, three groups of decreasing magnitude. A long deep sigh is followed, as from a relieved breast, by an already much more gentle and half calm prayer; and this again by the believing joy which anticipates the certainty of being answered. This song as it were casts up constantly lessening waves, until it becomes still as the sea when smooth as a mirror, and the only motion discernible at last is that of the joyous ripple of calm repose.