From First and Second Timothy, Titus by George T. Montague, SM, commenting on Titus 2:12:
In the Old Testament training most often meant educating children in the law of God and disciplining them, even punishing them (Deut 21:18; Sir 7:23), something that God himself does for his children (Deut 8:5; Prov 3:11–12; Heb 12:5–11). In the opinion of some authors, Paul is thinking of the severe physical discipline accompanying education in the Greek world and implying that the cross and suffering is the way Christians get trained. But here it is grace that educates. The thought is very Pauline: in the face of God’s overwhelming kindness shown in Jesus Christ, one cannot help but be transformed, for one is gazing on his brilliant glory through the power of the Holy Spirit (2 Cor 3:18). The energy comes more from awareness of God’s love than from his commands or the trials he sends. Suffering itself is of no avail for transformation unless its darkness is bathed in the overwhelming light of God’s love and grace.
The effect of this transforming light is first of all to bring about in the believer a decisive rejection of its opposite: godless ways and worldly desires, the rebellion against God so characteristic of pagan life (Rom 1:18) and the accompanying passions, which Paul earlier calls the flesh (8:3–8; Gal 5:16) and 1 John 2:16 calls the lust of the flesh, the lust of the eyes, and worldly pride. Titus 2:12 may echo a baptismal formula recited by converts in the rite of initiation; it is similar to 2 Pet 1:4: “escaping from the corruption that is in the world because of evil desire.”
The positive effects of God’s training grace are threefold, expressed by three adverbs that, interestingly, address the three objects of charity: (1) Oneself: live temperately—temperance or self-control, highly regarded among the Greek ethicists, was also listed by Paul via another Greek word as one of the fruits of the Holy Spirit (Gal 5:23). (2) Others: justly—justice regulates one’s relationships with others. (3) God: devoutly—devotion or piety directs one’s relationship with God. That God’s grace could accomplish this in those who must live in this world corrupted by sin and ruled by Satan (2 Cor 4:4; John 17:15–16) is amazing indeed.