If we will glorify God, we must give up on pursuing our own glory. This is why we read in Psalm 115:1, "Not unto us, O LORD, not unto us, but unto thy name give glory, for thy mercy, and for thy truth's sake." Why is this?
You cannot seek your own glory and God's at the same time for several reasons. One reason is that God does not share his glory with others: "I am the LORD: that is my name: and my glory will I not give to another, neither my praise to graven images" (Isa. 42:8). This is consistent with the fact that there is only one true God, and to give glory to anyone or anything else would be to give worship to that which is not God.
But there is another reason. You will not trust in God as you ought if you do not first worship and glorify him. To worship and glorify God, not in a ritual way but sincerely, means that we see that God is worthy of our praise and worthy of glory. And to see that God is glorious means that we see God for who he is. And that of course means that we recognize what ought to be obvious: that God is God and we are not!
You see, as long as you are looking to yourself for meaning and significance and for the resources to make it through this life, you will not and cannot be looking to God. As long as you think that you are worthy, you will not see the worthiness of God. That is why we must first say, "Not unto us," before we say, "but unto thy name give glory."
For God to call us to glorify himself is not vainglory on his part - it is the most loving thing he could do for us. For to call us to glorify himself is to call us to see in him all the resources of mercy and truth (ver. 1). It is to call us to see that "our God is in the heavens: he hath done whatsoever he hath pleased" (ver. 3). In these times of uncertainty and abounding iniquity, what a comfort it is to place our hope in this God! But again, you won't hope and trust in God if you don't first worship him.
This is why the Psalms goes on to say: "O Israel . . . O house of Aaron . . . Ye that fear the LORD, trust in the LORD: he is their help and their shield" (ver. 9-11). We trust in what we worship. Do you struggle with anxiety and fear? Stop being in awe of the wind and the waves and stand in awe of the one who controls the wind and the waves! Worship God anew and you will learn to trust in him afresh.
And thank God, this trust is not ill-placed. Those who trust in him will never be disappointed (cf. Rom. 10:11). And hence the Psalmist writes, "The LORD hath been mindful of us: he will bless us; he will bless the house of Israel; he will bless the house of Aaron. He will bless them that fear the LORD, both small and great" (ver. 12-13). Worship leads to trust and trust leads to blessing. So let us "bless the LORD from this time forth and forevermore. Praise the LORD" (ver. 18).