Below is an excerpt from Charles Hodge‘s systematic theology textbook on sanctification or moral/spiritual growth. He says more on this process in the same chapter, but here he simply talks about the method of sanctification. Here’s my summary of his six points:

1. The preaching of the gospel and the Holy Spirit lead the individual convert to Christ, who promises to save his people from sin.
   
2. Faith leads to union with Christ which essentially has two effects:
   
   1. You receive Christ’s merits. His crucifixion is your death and his resurrection is your life.
      
   2. You receive the Holy Spirit who helps you to grow in love for God and neighbor.
      
3. God’s Holy Spirit helps you apply your knowledge of the gospel to your own life, thus transforming your character over time.
   
4. God gives you daily opportunities to exercise your graces or the character traits of Christ and you are to look for those opportunities and practice those traits as the opportunity arises. Richard Foster once recommended praying each morning, “Lord, give me an opportunity to serve somebody in the name of Jesus today.”
   
5. Being a part of the church community gives the faithful access to God’s grace in very tangible ways: God’s people, the Lord’s Supper, Baptism, the preaching of the word, etc are means of grace.
   
6. Christians should practice God’s presence as they face the challenges of the day.
   

Hodge on Sanctification

1. The Soul is led to exercise Faith
   It is led to exercise faith in the Lord Jesus Christ, to receive Him as its Saviour, committing itself to Him to be by his merit and grace delivered from the guilt and power of sin. This is the first step, and secures all the rest, not because of its inherent virtue or efficacy, but because, according to the covenant of grace, or plan of salvation, which God has revealed and which He has pledged Himself to carry out, He becomes bound by his promise to accomplish the full salvation from sin of every one who believes
   
2. The Effect of Union with Christ
   The soul by this act of faith becomes united to Christ. We are in Him by faith. The consequences of this union are:
   
   1. Participation in his merits. His perfect righteousness, agreeably to the stipulations of the covenant of redemption, is imputed to the believer. He is thereby justified. He is introduced into a state of favour or grace, and rejoices in hope of the glory of God. (Romans 5:1–3.) This is, as the Bible teaches, the essential preliminary condition of sanctification. While under the law we are under the curse. While under the curse we are the enemies of God and bring forth fruit unto death. It is only when delivered from the law by the body or death of Christ, and united to Him, that we bring forth fruit unto God. (Romans 6:8; 7:4–6.) Sin, therefore, says the Apostle, shall not reign over us, because we are not under the law. (Romans 6:14.) Deliverance from the law is the necessary condition of deliverance from sin. All the relations of the believer are thus changed. He is translated from the kingdom of darkness and introduced into the glorious liberty of the sons of God. Instead of an outcast, a slave under condemnation, he becomes a child of God, assured of his love, of his tenderness, and of his care. He may come to Him with confidence. He is brought under all the influences which in their full effect constitute heaven. He therefore becomes a new creature. He has passed from death to life; from darkness to light, from hell (the kingdom of Satan) to heaven. He sits with Christ in heavenly places. (Eph. 2:6.)
      
   2. Another consequence of the union with Christ effected by faith, is the indwelling of the Spirit. Christ has redeemed us from the curse of the law by being made a curse for us, in order that we might receive the promise of the Holy Ghost. (Gal. 3:13, 14.) It was not consistent with the perfections or purposes of God that the Spirit should be given to dwell with his saving influences in the apostate children of men, until Christ had made a full satisfaction for the sins of the world. But as with God there are no distinctions of time, Christ was slain from the foundation of the world, and his death availed as fully for the salvation of those who lived before, as for that of those who have lived since his coming in the flesh. (Romans 3:25, 26; Heb. 9:15.) The Spirit was given to the people of God from the beginning. But as our Lord says (John 10:10) that He came into the world not only that men might have life, but that they might have it more abundantly, the effusion, or copious communication of the Spirit is always represented as the great characteristic of the Messiah’s advent. (Joel 2:28, 29; Acts 2:16–21; John 7:38, 39.) Our Lord, therefore, in his last discourse to his disciples, said it was expedient for them that He went away, for “if I go not away, the Comforter (the Παράκλητος, the helper) will not come unto you; but if I depart, I will send Him unto you.” (John 16:7.) He was to supply the place of Christ as to his visible presence, carry on his work, gather in his people, transform them into the likeness of Christ, and communicate to them all the benefits of his redemption. Where the Spirit is, there Christ is; so that, the Spirit being with us, Christ is with us; and if the Spirit dwells in us, Christ dwells in us. (Romans 8:9–11.) In partaking, therefore, of the Holy Ghost, believers are partakers of the life of Christ. The Spirit was given to Him without measure, and from Him flows down to all his members. This participation of the believer in the life of Christ, so that every believer may say with the Apostle, “I live; yet not I, but Christ liveth in me” (Gal. 2:20), is prominently presented in the Word of God. (Romans 6:5; Romans 7:4; John 14:19; Col. 3:3, 4.) The two great standing illustrations of this truth are the vine and the human body. The former is presented at length in John 15:1–8; the latter in 1 Corinthians 12:11–27; Romans 12:5; Ephesians 1:22, 23; 4:15, 16; 5:30; Colossians 1:18; Col. 2:19; and frequently elsewhere. As the life of the vine is diffused through all the branches, sustaining and rendering them fruitful; and as the life of the head is diffused through all the members of the body making it one, and imparting life to all, so the life of Christ is diffused through all the members of his mystical body making them one body in Him; having a common life with their common head. This idea is urged specially in Ephesians 4:15, 16, where it is said that it is from Christ that the whole body fitly joined together, through the spiritual influence granted to every part according to its measure, makes increase in love. It is true that this is spoken of the Church as a whole. But what is said of Christ’s mystical body as a whole is true of all its members severally. He is the prophet, priest, and king of the Church; but He is also the prophet, priest, and king of every believer. Our relation to Him is individual and personal. The Church as a whole is the temple of God; but so is every believer. (1 Cor. 3:16; 6:19.) The Church is the bride of Christ, but every believer is the object of that tender, peculiar love expressed in the use of that metaphor. The last verse of Paul Gerhardt’s hymn, “Ein Lammlein geht und tragt die Schuld,” every true Christian may adopt as the expression of his own hopes:—”Wann endlich ich soll treten ein In deines Reiches Freuden, So soll diess Blut mein Purpur seyn, Ich will mich darein kleiden; Es soll seyn meines Hauptes Kron’ In welcher ich will vor den Thron Des hochaten Vaters gehen, Und dir, dem er mich anvertraut, Als eine wohlgeschmückte Braut, An deiner Seiten stehen.”
      
3. The Inward Work of the Spirit
   The indwelling, of the Holy Spirit thus secured by union with Christ becomes the source of a new spiritual life, which constantly increases in power until everything uncongenial with it is expelled, and the soul is perfectly transformed into the image of Christ. It is the office of the Spirit to enlighten the mind: or, as Paul expresses it, “to enlighten the eyes of the understanding” (Eph. 1:18), that we may know the things freely given to us of God (1 Cor. 2:12); i.e., the things which God has revealed; or, as they are called in v. 14, “The things of the Spirit of God.” These things, which the natural man cannot know, the Spirit enables the believer “to discern,” i.e., to apprehend in their truth and excellence; and thus to experience their power. The Spirit, we are taught, especially opens the eyes to see the glory of Christ, to see that He is God manifest in the flesh: to discern not only his divine perfections, but his love to us, and his suitableness in all respects as our Saviour, so that those who have not seen Him, yet believing on Him, rejoice in Him with joy unspeakable and full of glory. This apprehension of Christ is transforming; the soul is thereby changed into his image, from glory to glory by the Spirit of the Lord. It was this inward revelation of Christ by which Paul on his way to Damascus was instantly converted from a blasphemer into a worshipper and self-sacrificing servant of the Lord Jesus. It is not, however, only one object which the opened eye of the believer is able to discern.
   

   The Spirit enables him to see the glory of God as revealed in his works and in his word; the holiness and spirituality of the law; the exceeding sinfulness of sin; his own guilt, pollution, and helplessness; the length and breadth, the height and depth of the economy of redemption; and the reality, glory, and infinite importance of the things unseen and eternal The soul is thus raised above the world. It lives in a higher sphere. It becomes more and more heavenly in its character and desires. All the great doctrines of the Bible concerning God, Christ, and things spiritual and eternal, are so revealed by this inward teaching of the Spirit, as to be not only rightly discerned, but to exert, in a measure, their proper influence on the heart and life. Thus the prayer of Christ (John 17:17), “Sanctify them through thy truth,” is answered in the experience of his people.
   

4. God calls the Graces of his People into Exercise
   The work of sanctification is carried on by God’s giving constant occasion for the exercise of all the graces of the Spirit. Submission, confidence, self-denial, patience, and meekness, as well as faith, hope, and love, are called forth, or put to the test, more or less effectually every day the believer passes on earth. And by this constant exercise he grows in grace and in the knowledge of our Lord and Saviour Jesus Christ. It is, however, principally by calling his people to labour and suffer for the advancement of the Redeemer’s kingdom, and for the good of their fellow-men, that this salutary discipline is carried on. The best Christians are in general those who not merely from restless activity of natural disposition, but from love to Christ and zeal for his glory, labour most and suffer most in his service.
   
5. The Church and Sacraments as means of Grace
   One great end of the establishment of the Church on earth, as the communion of saints, is the edification of the people of God. The intellectual and social life of man is not developed in isolation and solitude. It is only in contact and collision with his fellow-men that his powers are called into exercise and his social virtues are cultivated. Thus also it is by the Churchlife of believers, by their communion in the worship and service of God, and by their mutual good offices and fellowship, that the spiritual life of the soul is developed. Therefore the Apostle says, “Let us consider one another, to provoke unto love and to good works: not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another; and so much the more as ye see the day approaching.” (Heb. 10:24, 25.)
   

   The Spirit renders the ordinances of God, the word, sacraments, and prayer, effectual means of promoting the sanctification of his people, and of securing their ultimate salvation These, however, must be more fully considered in the sequel.
   

6. The Kingly Office of Christ
   In this connection, we are not to overlook or undervalue the constant exercise of the kingly office of Christ. He not only reigns over his people, but He subdues them to Himself, rules and defends them, and restrains and conquers all his and their enemies. These enemies are both inward and outward, both seen and unseen; they are the world, the flesh, and the devil. The strength of the believer in contending with these enemies, is not his own. He is strong only in the Lord, and in the power of his might. (Eph. 6:10.) The weapons, both offensive and defensive, are supplied by Him, and the disposition and the skill to use them are his gifts to be sought by praying without ceasing. He is an ever present helper. Whenever the Christian feels his weakness either in resisting temptation or in the discharge of duty, he looks to Christ, and seeks aid from Him. And all who seek find. When we fail, it is either from self-confidence, or from neglecting to call upon our ever present and almighty King, who is always ready to protect and deliver those who put their trust in Him. But there are dangers which we do not apprehend, enemies whom we do not see, and to which we would become an easy prey, were it not for the watchful care of Him who came into the world to destroy the works of the devil, and to bruise Satan under our feet. The Christian runs his race “looking unto Jesus;” the life he lives, he lives by faith in the Son of God; it is by the constant worship of Christ; by the constant exercise of love toward Him; by constant endeavours to do his will; and by constantly looking to Him for the supply of grace and for protection and aid, that he overcomes sin and finally attains the prize of the high-calling of God.