How can one seek the righteousness of God?
At the core of the Christian Gospel, it has been revealed to mankind that the one true God of the universe is perfectly righteous in every respect, in all that He does, and that humans are innately unrighteous. Because of the fall of mankind in the Garden of Eden, we no longer have an intact relationship with God by default of being one of his created humans; He and His ways are flawless perfection, and therefore, His standards of relationship require the same, which humans fall terribly short of.
The 1st definition that Webster's Dictionary gives to define righteousness is: "to act in accord with divine or moral law: free from guilt or sin." To seek to be righteous is to attempt to conduct all of one's thoughts and actions so that no fault can be found inside, or outside, the person. From strictly a human viewpoint, it is possible for us to do good deeds apart from God that have no obvious or visible blemishes of sin or evil. However, it is not possible for us to do good deeds with irreproachable motives, nor is it possible to do only good deeds, and do them continuously, without eventually doing wrong. In addition to this, it is also true that before the intent to even start doing good is begun, all humans have a grimy, mistake-ridden past that we would rather not acknowledge, even to ourselves, which causes the entire endeavor of pursuing righteousness to be fatally flawed before it's begun.
Most of mankind in our age assents to the following philosophy: a good deed can be entirely good, and therefore, while we may not be perfect, we certainly are not all that bad, or not as bad as some people, and sometimes we are good, and so perhaps even "righteous." It's at least a consistent hypothesis, except that it only compares bad people to bad people — there is no sample group of good people. This paradigm of right and wrong takes no account of how fallen we are on the inside; that if we should seek to do good deeds, we are still operating from a disposition of pride, selfishness or another similar human attitude or frame of mind and heart. We can't do it. Jesus revealed this to mankind with some examples that magnify the concept of our depravity, and drug it tumultuously struggling, into plain sight and to our attention. In one such example, the story of the rich young ruler, the wealthy young man's thoughts were on what he could accomplish to gain God's approval. The rich young ruler asked, "...Teacher, what good thing shall I do that I may obtain eternal life?" (see: Matthew 19:16-26). This man's focus was on what he could do in the power of his own sinful nature, a nature of which God tells us is only capable of evil: "...and that every intent of the thoughts of his heart were only evil, continually" (Genesis 6:6). Jesus spoke towards a correction of thought, illustrating that no increased level of "performance" or "good work" can have a high-enough appraisal of value with regards to earning God's approval. Being divine, Jesus saw this man's inward desires and thoughts, and made a request of the rich young ruler, tailored to confront the most precious object of his heart — his wealth — and then directed the logical momentum of the conversation towards the only potential alternative, an alien righteousness, viz. himself, the Christ. "'...All these things I have kept; what am I still lacking?' Jesus said to him, 'If you wish to be complete, go and sell your possessions and give to the poor, and you will have treasure in heaven; and come, follow Me.'" (Matthew 19:20-21). Christ's most dedicated followers even abandoned Him when He was arrested and prosecuted. We can't do it. We need an alien righteousness; we need a righteousness outside of ourselves.
What is the rational response to this hopeless condition? We are left with an untenable position in the matter of righteousness before God. The Bible says that when we believe in Christ, all that Christ is replaces our own account of failure, pride, sin, and "not good enough." To seek the righteousness of God is to be in the process and possession of sanctification. Sanctify is the word used in the Bible to describe this ongoing work that God starts inside a believer when he or she has given up on their own efforts to earn God's approval and believes in Christ's finished work on his or her behalf. To sanctify is to make a saint, which is to become more righteous, and so, to be continuously improved. To clearly understand sanctification, let's use two doctrinal terms that will help illuminate this work that God performs on his born-again children.
Progressive Sanctification is what God performs on every believer. A Christian has the Holy Spirit living inside them at the moment that they are born again performing the work of sanctification until they leave this earth. "...And he will give you another Helper, to be with you forever, even the Spirit of truth, whom the world cannot receive, because it neither sees him nor knows him. You know him, for he dwells with you, and will be in you." (John 14:16).
Positional sanctification makes reference to our status of perfection before God. We are imperfect at the moment, but slowly becoming more perfect, which in this human body we never reach the final completion of. The concept of positional sanctification is that God declares a verdict of righteous in His sight, so that when He looks at imperfect sinners who have accepted Christ, He sees perfection in us, and treats us as such.
To believe in Christ is to have sought His righteousness and to have attained it (positionally) and be moving more and more towards its perfection (progressively). Second Corinthians 6:4 says, "For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God." To pursue the righteousness that you have obtained through Christ is to continue in His work of sanctification. First Thessalonians 4:3 states, "For this is the will of God, your sanctification..." A key to a successful pursuit of sanctification is for a believer to pursue a cooperative lifestyle with the Spirit of Gods' work, and not fight against it. Some quintessential items to a lifestyle that is pleasing to God's spirit are: regular fellowship with other believers (joining and attending church events), reading God's word, praying, giving, doing good deeds, and by abstaining from sin, idols, and lust, as best as you understand how.
As believers, when we attend to keep in step with God's spirit, we receive the best life that God affords to his children here on earth. Matthew 6:33 says to us, "But seek first His kingdom and His righteousness, and all these things will be added to you." Matthew 6:33 is making reference to essential needs in this life, such as food, clothes, housing, and proper health care, but the context also intimates that "these things" are also the blessings of God which cannot be limited to the human imagination. Such things could be a scholarship to a desired school, or perhaps a possession that brings you joy, a job, a toy, a vacation, a skill that you didn't know you had, a spouse, a child etc. Christians have the righteousness of Christ to their account, and their lives should be marked more so by the contentment that this eternal truth brings and marked less so by a rigorous, competitive pursuit of riches and pleasure. Christian lives should be lived in fellowship with like-minded Christians, trusting that God will provide and reward them for their trust and belief. Hebrews 11:6 says that, "...for he who comes to God must believe that He is and that He is a rewarder of those who seek Him."