There's a story in the Old Testament that has taught me several important lessons about living my life centered around God. Through the rise and fall of King Hezekiah, I have seen that when God is the center of our lives, our prayers reflect a concern for His name and glory, our definition of God's blessing changes, and our circumstances show us how we're doing. 
Praying for God's glory
When the king of Assyria threatens to attack God's people, Hezekiah prays to God for deliverance. Notice his primary concern, at the end of his prayer in 2 Kings 19:14-19:
Now, O LORD our God, I pray, deliver us from his hand that all the kingdoms of the earth may know that You alone, O LORD, are God."
2 Kings‬ ‭19‬:‭19‬ NASB
Hezekiah comes to God zealous for the reputation of God, and sees the oppression of His people as an opportunity for God to vindicate His great name and demonstrate His great might. He does ask for deliverance, but his motivation is what is truly striking: he asks for deliverance because he wants God's reputation to increase in the world.
This reminds me of David's indignant attitude when he heard that a Philistine had "taunted the armies of the living God." (1 Samuel 17:26) David found the courage to fight Goliath because he saw that what was at stake in the battle was actually the glory and honor of God among His people. Just like Moses didn't want to give the Egyptians any cause to speak evil of God (Exodus 32:12), a great man of God is always concerned with the name of the Lord and whether it's being reverenced. 
This brought the question to my mind: Do I see the trials in my life as opportunities for God's name to be exalted? The name and the glory of God is what hangs in the balance in my life, and in every trial. We see that clearly in the conversation between God and Satan in Job 1:6-12 (it's worth looking up this interchange when you have a moment). 
One way to know how I view my trials is to examine how I pray. When I seek deliverance, why am I seeking it? Am I mindful of how the situation reflects on the Lord, as Hezekiah, David, and Moses, about what it says about the One Who I claim to be my God and Refuge and Defender? Do I see these micro-moments as having eternal implications? Or am I only fixated on the here and now? Just concerned with me, my reputation, my comfort, and only this moment?
More and more, I want to pray for God to use my life and all the circumstances of it have opportunities to vindicate Himself and His great name -- to use everything in my life to prove how wonderful He is, how blessed it is to walk with Him, how tender and loving He is as a Father, the fullness of grace and salvation that belongs in Christ. Am I living on THAT scale?
This is part of what it means to live a God-centered life: praying God-centered prayers. 
The consequences of neglecting God's glory in prayer 
Sadly, Hezekiah doesn't continue to be an example of God-centered prayer. His own life, comfort, and will creep in as the primary motivation in his prayers.
Contrast his earlier prayer with a prayer later in his life, when Isaiah tells him he is going to die of a sickness:
"Remember now, O LORD, I beseech You, how I have walked before You in truth and with a whole heart and have done what is good in Your sight." And Hezekiah wept bitterly. (‭2 Kings‬ ‭20‬:‭3‬ NASB)
He's basically feeling sorry for himself, pleading his own case and merits before the Lord. It's not that it's wrong to ask God for help --  not at all! God is a loving Father Who certainly wants us to come to Him for every need -- but it's clear that Hezekiah's motivation has completely changed. He doesn't even mention God's reputation and glory in his prayer this time around. He doesn't submit his own desires to the will of God, but bitterly mourns and bargains with God instead.
God ended up answering his prayer (v6), but we see that it's during this "bonus time" that two terrible things happened:
- all of the treasuries of Israel would be robbed by Babylon, (At that time Berodach-baladan a son of Baladan, king of Babylon, sent letters and a present to Hezekiah, for he heard that Hezekiah had been sick. (‭2 Kings‬ ‭20‬:‭12‬ NASB))
- his son Manasseh was conceived, a horrible king who "seduced them to do evil more than the nations whom the Lord destroyed before the sons of Israel. (2 Kings 21:9)"
We see striking evidence that his focus completely shifted later in his life: 
'Behold, the days are coming when all that is in your house, and all that your fathers have laid up in store to this day will be carried to Babylon; nothing shall be left,' says the Lord. 'Some of your sons who shall issue from you, whom you will beget, will be taken away; and they will become officials in the palace of the king of Babylon.'" Then Hezekiah said to Isaiah, "The word which you have spoken is good." For he thought, "Is it not so, if there will be peace and truth in my days?" (2 Kings 20:17-19)
He had changed so much that he was no longer concerned with the name of the Lord, or even the welfare of his own sons, but only whether his days were comfortable. The scale he was considering was so much smaller, to the point that he had stopped being concerned with how God's glory was reflected in his circumstances, but only with how he felt in his life. 
So we see the contrasting true fruit of a self-centered prayer -- which is not in reality what it probably looked like to Hezekiah at the time (an immediate affirmative answer and life extension ("wow, God must be happy with me!")) -- but rather it produced unexpected evil that may have never otherwise occurred. 
We have to be spiritually minded to pray God-centered prayers, and also to judge the fruit of our prayer life and discern which answers are true "blessings."
Our definition of blessing changes
Seeing this changed how I define what constitutes God's blessings in my life. As David said,
Deal bountifully with Your servant, 
That I may live and keep Your word. 
Psalms‬ ‭119‬:‭17‬ NASB
God's true blessing, how He deals bountifully with me, is that He enables me to live a life pleasing to Him. 
This is the bountiful dealing that Habakkuk must have had with God, that he could look upon everything that had failed in the physical world around him and yet say, "He has made my feet like hinds' feet, and makes me walk on my high places." (see Habakkuk 3:17-19)
How is it possible that despite all going wrong, Habakkuk can say this? He must have seen God's true bounty was in helping him keep His word. And so, despite all the was going wrong in his life externally, he could exalt God's strength and declare His salvation. 
And in that case, no matter what happens to me externally, if I heed the Lord and observe His commands, I can say "Wow, He has dealt bountifully with me because He has helped me keep His word."
Circumstances show us how we're doing
The Bible tells us why God allowed these things to happen to Hezekiah:
Even in the matter of the envoys of the rulers of Babylon, who sent to him to inquire of the wonder that had happened in the land, God left him alone only to test him, that He might know all that was in his heart.
‭2 Chronicles‬ ‭32‬:‭31‬ NASB
God allows such circumstances into our lives to see how we will respond. 
I can imagine the Lord wondering, "When the strong Assyrian army comes against him, what will he be concerned about? ... Wow, he was still concerned with My Name? Great! I'll deliver him miraculously!" And again, a little while later, God thinking, "What if a terrible sickness comes against him, what will he be concerned about? ... His life and his comfort only? He forgot about My Name? Wow, I had really hoped for something better...."
God is searching the earth to see who truly belongs to Him, and trials are one way He reveals the character of our hearts. 
I can expect the same of the trials which I face, and it is good to examine: what do my circumstances reveal about what my life revolves around? When a challenge comes, is my primary concern for the name and glory of the Lord, or is there a tenderness somewhere deep in my heart for myself, my life, and my reputation? 
Each of the circumstances I face is a test that shows God, and shows me, whether I'm rooted in the here and now -- in my physical existence -- or whether I'm a true Christian, anchored in the spiritual realm and concerned with eternal things: God's name being honored, His will being done, and His kingdom coming.