The apostle Paul wrote to Titus, "For the grace of God that brings salvation has appeared to all men, teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly in the present age" (Titus 2:11-12). In these words are found the response of every Christian to the gift of grace. We have the hope of salvation because of what God has granted to us. Our response is an ordering of our lives: "we should live soberly, righteously and godly."
The definition of the word godly is minimally helpful. The term refers to piety, devotion and reverence. More helpful are the verses that describe the kind of life that characterizes the Christian profession. For example, when considering the proper role model for a godly life, we consider Jesus Himself. Peter wrote, "But as He who called you is holy, you also be holy in all your conduct, because it is written, 'Be holy, for I am holy'" (1 Peter 1:15-16). Jesus was guileless (cf. 1 Peter 2:21-24), and pure (cf. 1 John 3:1-3). In His life, and in His death, He always sought to do the will of His Father in heaven (cf. John 15:10).
A truly godly life is an informed one. Paul wrote about the Jews, who "have a zeal for God, but not according to knowledge. For they being ignorant of God's righteousness, and seeking to establish their own righteousness, have not submitted to the righteousness of God" (Romans 10:2-3). In order for us to live a godly life, we have to know what God considers godly. Fortunately, He has revealed these things to us in scripture.
So, simply put, a godly life is a life that is lived in accord with God's expressed will. The Psalmist wrote, "Teach me, O Lord, the way of Your statutes, and I shall keep it to the end. Give me understanding, and I shall keep Your law; indeed, I shall observe it with my whole heart. Make me walk in the path of Your commandments, for I delight in it. Incline my heart to Your testimonies, and not to covetousness. Turn away my eyes from looking at worthless things, and revive me in Your way" (119:33-37). He contrasts God's way with "worthless things," and contrasts God's testimonies with covetousness. God's will is the antithesis of evil. His way is the way of godliness. Consider these words: "How sweet are Your words to my taste, Sweeter than honey to my mouth! Through Your precepts I get understanding; Therefore I hate every false way. Your word is a lamp to my feet and a light to my path" (119:103-105).
So, we seek to emulate our Lord. We seek direction from God to know what is right and wrong. And, as we attain such knowledge, it is important that we dwell upon it. Paul wrote the Philippians, "Finally, brethren, whatever things are true, whatever things are noble, whatever things are just, whatever things are pure, whatever things are lovely, whatever things are of good report, if there is any virtue and if there is anything praiseworthy - meditate on these things. The things which you learned and received and heard and saw in me, these do, and the God of peace will be with you" (Philippians 4:8-9). Meditation on what is righteous, in contrast with the pablum of popular culture, helps to direct the Christian's path in the way of godliness. The man whose mind dwells in the muck of worldliness will be corrupted in his walk.
Finally, a godly walk is a motivated walk. It is easy to become distracted by the tedium of this life. We can become "shortsighted, even to blindness" (cf. 2 Peter 1:9). In fact, Peter's statement is made within the context of adding virtuous characteristics (including godliness, vs. 6), to ensure we don't suffer from that myopia that would endanger our eternal standing before God. As Paul put it, "Brethren, I do not count myself to have apprehended; but one thing I do, forgetting those things which are behind and reaching forward to those things which are ahead, I press toward the goal for the prize of the upward call of God in Christ Jesus" (Philippians 3:13-14). A disciplined Christian, seeking always to do all and only what God allows, will most certainly attain the prize he seeks.
A righteous life is attainable with effort and focus. Such godliness is wonderfully profitable, "For bodily exercise profits a little, but godliness is profitable for all things, having promise of the life that now is and of that which is to come" (1 Timothy 4:8). Later in the same epistle, Paul wrote, "Now godliness with contentment is great gain" (6:6). If we remember that this life is preparatory to eternity, we will answer the call of grace with a life that is lived in accord with God's righteousness.