In our text, God is speaking, prophetically, to His people, who will be experiencing captivity at the hands of the Babylonians. It will not be pleasant. The bondage will seem permanent. The oppressor will seem unconquerable. But God is telling them that He has always had other, better plans for Israel (Isaiah 2:1-5). He has not / will not change His mind. The promises and plans of God are / will be still in effect. The oppressor shall be removed. Israel shall be restored. These plans are so wonderful that they can also encourage us today. The blessings that God has for Israel will also bring blessing on the whole world (Genesis 12:1-3; Isaiah 60:1-3; Habakkuk 2:14). Therefore, whatever it is that is oppressing us presently is of temporary nature. Whatever threatens the prosperity of Christ's gospel and kingdom will not prosper. Though a dark season may be upon us, the dawn of a glorious morning is ahead of us (Psalm 30:1-5; 130:5-8; Romans 13:11-12; II Thessalonians 1:3-10; Titus 2:11-13).
Let's look at the encouragement that God is giving Israel, so that we, too, can be encouraged.
Look to the beginning of your story - Isaiah 51:1-3
God started with two elderly people that He called to follow Him - Abraham and Sarah. He gave them promises to have children in their old age, who would multiply into a great nation that would prosper and be a blessing to the whole earth. God established Abraham by faith in those promises. We, too, have a starting point in that story. By faith in the promises of the Gospel, we are called children of Abraham (Galatians 3:6-29).
Listen to God - Isaiah 51:4-6
God has spoken. His Word is law! His promises do not change (Isaiah 46:9-11). His power (my arms) will bring forth salvation to His people (I Peter 1:3-5). The world is going to be dissolved, but God's people are going to preserved (II Peter 3:10-13).
Let not your heart be troubled by men - Isaiah 51:7-8
Men are bold now, but they will soon be gone, as if moths ate them like cloth, or worms infested wool. Men are short-lived, fragile beings - vulnerable to many weaknesses. Compared to God, who is eternal, all-powerful and all-wise, men should not dominate our thoughts and emotions (Isaiah 2:22; 8:9-13; 12:1-2; John 14:27; 16:33).
Let God hear your voice - Isaiah 51:9-11
This portion is a prayer. Calling on "The Arm of the Lord" is a call for action and for strength to be shown. This prayer is expressed as if God were asleep and we are waking Him up. God does not actually sleep (Psalm 121:4), but we should speak to Him urgently, as if He needed to be awakened to handle an important matter (Psalm 7:6; 9:19; 10:12; 17:13; 44:23; 68:65-66; Luke 18:1-8). In prayer, we may rehearse to God His great works of the past (e.g. deliverance from Rahab / Egypt, the parting of the Red Sea). We may also claim the promises of future blessings (Isaiah 51:11 cp. 2:1-5; 12:1-6).
Look to God, not to man - Isaiah 51:12-16
God reinforces what He has already said. Don't be afraid of man. They are like grass (temporary and fragile - Isaiah 40:6-8). Almighty God is your Savior. He has delivered you in the past. He will deliver you in the future (Psalm 56:1-13; II Corinthians 1:8-10; II Timothy 4:14-18). God has given you His Word. Keep yourself established in it (Romans 10:8-10; Colossians 3:16; I Timothy 4:13,15-16; II Timothy 3:15-17). His plan to establish Zion is not just a benefit for Israel, but for the whole world. Psalm 122:6-9 may be considered a prayer for the future Israel - when Christ comes and establishes His Kingdom and there is true peace on earth (Psalm 48:1-2).