They have seen thy goings, O God! This verse may refer to processions of a warlike kind, or to such as are made in times of peace by those who give thanks for victory. It is customary for the people of God, on occasions of the latter description, to go forth and present peace-offerings in the temple. This has led some to understand by the goings of God, [1] the crowds of his people when they proceed to the temple. But I am disposed to think that God himself is here represented as a king leading and marshalling forth his armies. Accordingly, it is added, in the sanctuary, under which expression there is an apt allusion to the visible symbol of the Divine presence. The great reason why God undertakes the guardianship of his people, and goes before them to repel the attacks of the enemy, is his having promised that he will hear their prayers in the sanctuary. He is therefore described as if he were seen coming out of his holy habitation, that he might conduct his people to victory. David calls him his King, to divert the attention of the people from himself, and lead them to view a name which belonged to a frail mortal man such as he was, in its higher application to the supreme Head of all. He speaks, it is true, in the name of the people, but not to the exclusion of himself.

Footnotes

1 - "This doubtless refers to the order of the procession then on its march, and to that of religious processions in general. In the religious and festal processions of the Hindoos there is the same order and classes of performers. The singers, men and women, precede, singing songs appropriate to the occasion; and then the players on instruments follow after." -- Illustrated Commentary upon the Bible.

They have seen thy goings, O God - That is, the lookers on in the solemn procession referred to in Psalm 68:25; or, in other words, Thy goings have been attended by pomp and magnificence, and have been witnessed by multitudes. The word "goings" here refers to the solemn triumphal processions which celebrated the victories achieved by God.
Even the goings of my God, my King - The psalmist here speaks of God as "his" God and "his" King. The idea seems to have suddenly crossed his mind that this great God, so glorious, is "his" God. He exults and rejoices that He whom he adores is such a God; that a God so great and glorious is "his." So the believer now, when he looks upon the works of God, when he contemplates their vastness, their beauty, and their grandeur, is permitted to feel that the God who made them is "his" God; to find consolation in the thought that his "Father made them all."
"He looks abroad into the varied field
Of Nature, and, though poor, perhaps, compared
With those whose mansions glitter in his sight,
Calls the delightful scenery all his own.
His are the mountains, and the valleys his,
And the resplendent rivers; - his to enjoy
With a propriety that none can feel
But who, with filial confidence inspired,
Can lift to heaven an unpresumptuous eye,
And smiling say, 'My Father made them all!'
Are they not his by a peculiar right,
And by an emphasis of interest his,
Whose eye they fill with tears of holy joy,
Whose heart with praise, and whose exalted mind
With worthy thoughts of that unwearied love
That plann'd, and built, and still upholds a world
So clothed with beauty for rebellious man?"
task, Book v.
In the sanctuary - Or, "to" the sanctuary; in other words, as the ark was borne to the sanctuary, the place appointed for its rest, for, as above remarked, the psalm seems to have been composed on such an occasion.

They have seen thy goings - These kings of the Amorites have seen thy terrible majesty in their discomfiture, and the slaughter of their subjects.

They have seen (s) thy goings, O God; [even] the goings of my God, my King, in the sanctuary.
(s) That is, how you who are chief King goes out with your people to war, and gives them the victory.

They have seen thy goings, O God,.... In saving his people, and destroying his enemies;
even the goings of my God, my King, in the sanctuary; the walk and conversation of Christ, when he was made flesh, and dwelt among men; his manner of life and deportment; his works and miracles, his sufferings, death, and resurrection from the dead; all which his apostles were eyewitnesses of; as also his going up to heaven, which was visible to angels and men; likewise his progress and victorious expeditions in Judea, and in the Gentile world, by the ministry of the word, in which he went forth conquering, and to conquer; which sense is confirmed by the following words: for Christ, who is God over all, the Lord and God of his people, and King of saints, is here, as throughout the psalm, intended. The Targum interprets it of the path or goings of the divine Majesty upon the sea, which the house of Israel saw.

The triumphal procession, after the deliverance, is depicted.
They have seen--impersonally, "There have been seen."
the goings of my God--as leading the procession; the ark, the symbol of His presence, being in front. The various bands of music (Psalm 68:25) follow, and all who are--

They - Men saw and observed it. Goings - The procession of the ark to Zion, the solemnity whereof is particularly described in the following verses. The sanctuary - The tabernacle prepared for it.