77:10-15 Verse 10 means the psalmist felt his sorrow stemmed from God's withdrawing His powerful right hand from his life. In other words God was not answering his prayers and coming to his aid as He had done in the past.
This remembrance led Asaph to concentrate on God's great acts for His people in the past. God's way is holy (v. 13) in that it is different from the ways of men. Yahweh is unique among the so-called gods of the nations. He had done mighty deeds and performed great miracles for Israel in the past. The greatest example of this is the Exodus when the Lord redeemed the sons of Jacob and Joseph. Perhaps the writer described the Israelites this way to draw attention to their unworthiness.
77:16-18 These verses evidently describe the phenomena that accompanied the Exodus.
77:19-20 God used Moses and Aaron as shepherds to lead His people through the Red Sea to safety and liberty. However it was God Himself who provided the deliverance.
Even though he felt distressed, the psalmist found comfort and encouragement during his sleepless night by remembering God's powerful redemption of His people. This remembrance doubtless gave him hope for the future. God would again redeem His people from their enemies.