But they that wait upon the Lord shall renew their strength; they shall mount up with wings as eagles; they shall run, and not be weary; and they shall walk, and not faint. Isaiah 40:31
How do you renew your strength?
1Chronicles 16:11 Seek the LORD and his strength, seek his face continually.
Isaiah 30:15 For thus saith the Lord GOD, the Holy One of Israel; In returning and rest shall ye be saved; in quietness and in confidence shall be your strength: and ye would not.
God is our strength...
Psalms 18:2 The LORD is my rock, and my fortress, and my deliverer; my God, my strength, in whom I will trust; my buckler, and the horn of my salvation, and my high tower.
Isaiah 26:4 Trust ye in the LORD forever: for in the LORD JEHOVAH is everlasting strength:
Strength is a Gift of God...
Isaiah 40:29 He giveth power to the faint; and to them that have no might he increaseth strength.
Romans 5:6 For when we were yet without strength, in due time Christ died for the ungodly.
The amazing thing about the scripture you quoted is that it says we are to wait upon the Lord, and He will renew our strength. This infers that we can not renew our own strength on our own. In reality, we have no strength, or at least none, when compared to God. If you look at Isaiah 40:28, God demonstrates His strength by showing that He is the Creator. Our strength is limited, God's strength is infinite and He never grows weary.
So how do we renew our strength? If we renew strength, we would have had strength to begin with. What did we do originally to gain our spiritual strength? When we were dead in our trespasses and sins, we were weak. I don't know any strong dead people. But when we repented and trusted Jesus Christ's death, burial and resurrection for the forgiveness of our sins, we were born again, from God's Spirit. God then gave us His Holy Spirit which now gives us His strength. God is our strength. Apart from God we are spiritually dead.
Now strength infers that we need strength to do something. Notice again the passage. Mount up with wings of eagles. Run and not be weary. Walk and not faint. What do these things mean? If we need God's strength to accomplish these things, do you think it applies to regular day-to-day life that any non-saved person can do and not faint? I think these tasks (mount up, run, walk) have to do with our spiritual walk, which requires the strength of God to move forward from day to day.
Mount up with wings of eagles. We can't fly, but God can walk on water. Nothing is impossible with Him. Sometimes service to him means that we must do the impossible. How can we do something that is impossible for us to do in human strength? How did Joshua conquer so many nations? How did Gideon conquer the Midianites with only 300? How did Moses free a nation from slavery? It was only the strength of the Lord that did these mighty deeds, and it was only through waiting upon the Lord for clear instructions that any of these men accomplish the impossible. When we see mountains, let us wait upon the Lord, trusting that He will do the impossible in our lives, and our strength shall be renewed.
Run and not be weary. Many times we are called to minister to others, and it becomes a race to serve. Serving at the job, serving at home, serving at the church, serving the Lord through your ministry, etc. It sometimes becomes overwhelming and we start to tire. But the scripture says to wait for the Lord in the middle of these times and He will renew our strength. When we wait, we are trusting that His strength will come to move forward. Through reading the word, prayer, and worship, we are renewed. When we wait upon him, we trust that He will renew us and give us the strength to endure. And he does. He brings us through, day after day. One thing about waiting with expectation is that you are more alert to seeing the little things that God does, which leads to thanksgiving, praise, and worship. He will astound you when you quietly wait for Him, looking for Him to come through, even in the midst of daily life.
Finally, they shall walk and not be faint. How do you grow faint from walking unless you are very weak. It could be old age or it could be from dread. I picture the saints of God walking the course of life in their last days, walking and not growing faint, because they've had years of knowing how to wait upon the Lord. They think back on how far God has brought them, and where God is leading them, and in that they walk without being faint. And those saints who endured to the end in suffering, they too walked to their fate, looking forward to Christ, walking to their fate, not growing faint. Who wouldn't grow faint when being sent to a Lion's den, or to a fiery furnace? Those who wait upon the Lord, trusting in Him as their savior will not. During the hardest times, we walk through them, not growing faint, but being surrounded by the strength of God, and God Himself proves His word true, even to the death.
Seeking the Lord, and waiting for Him, this is how we renew our strength.