The people of God should always be talking about the many, many good things He has done for them. And, while they're doing that, while they're still thinking about how good and gracious He is, they'll also be in the best possible frame of mind to ask Him for the things they still need. In the psalm before us, David leads the worshippers in exactly that way: he begins with praise and thanksgiving, then he leads them to call on the goodness of God for what they still need.
It would do us well to follow David's lead. It would do us well to remember God's goodness at the very beginning of our prayers. Like David, we can sing, "I will praise You, O Lord, with my whole heart; I will tell of all Your marvelous works." We can and should follow this by being more specific about His blessings, as David does here. Then, finally, while still thinking about the goodness of God, we can go on to lay before Him our needs.
This prayer of David is a good example. He sings, "Have mercy on me, O Lord! Consider my trouble from those who hate me." We should be careful to notice that he goes on to express his confidence in God's care, based on what he had already said. He sings, "You Who lift me up from the gates of death, that I may tell of all Your praise in the gates of the daughter of Zion. I will rejoice in Your salvation." We too should first express our needs, then, based on what God has already done in our lives, we should also express our confidence in His care.
Like David, we can follow this with meditation. He thinks over what has happened to his enemies. We too should think over what has happened in our lives and see the way God has led. From this we can draw the conclusions that David draws: "The wicked shall be turned into hell, and all the nations that forget God, for the needy shall not always be forgotten; the expectation of the poor shall not perish forever." David is confident that his prayers WILL be granted, and, knowing how caring is our God, we too can be confident!
We can finally close our prayer as David does when he sings, "Arise, O Lord, do not let man prevail; let the nations be judged in Your sight. Put them in fear, O Lord, that the nations may know themselves to be but men." We might use different words. We might say something like, "Arise, O Lord, do not let them pass me over for the next promotion (or "Do not let me fail in this assignment," or "Don't let me fail in this work I have to do," or . . .)." Then we too can say, "let people be glad that I belong to You. Let them come to You also because of my witness to Your grace.