A big question to address in a small space! The simple definition of grace is God's favor. But what it means to receive such benevolence is demonstrated in boundless ways. As a child in religion class, I remember imagining grace as a birthday present in a brightly wrapped box with a big bow on top. That's because Sister told us grace is a gift, and the only gifts I'd ever seen looked like this.
The Old Testament describes God's favor differently. It's expressed in the act of creation, as well as the covenant with Israel, and the liberating force of Exodus. In the New Testament, Saint Paul rightly calls Jesus Christ the grace of God, using the Greek word charis, from which also comes charisma, the empowering gifts of the Spirit.
So how do we "get" grace, or know it when we see it operating? Divine grace comes to us through the mercy, forgiveness, and rescue of God at work in our lives. The classic definition of a sacrament is that of a sign rooted in Christ which provides grace. So add the sacraments of the Church to the ways in which we receive this gift. The Eastern Fathers went so far as to say that sacraments "divinize" us: God becomes flesh so that flesh can share in the divine life, including God's immortality.
In the West, Saint Augustine argued that grace heals and liberates our sin-inclined wills so that we can do the will of God. Without grace, we're literally lost. Saint Thomas Aquinas envisioned grace as elevating us to a higher level in closer union with God. Thomas Merton saw grace as the antidote to the "death dance" in our blood. The bottom line on all of these approaches to understanding grace—life-giving force, bonded relationship, liberating power, incarnation and participation in divine gifts, healing, uplifting, unifying, detoxifying—is that it comes to us free and unmerited. We can't earn it by obeying laws or racking up spiritual points. God doesn't "owe" us grace even if we're saintly every moment of the day. In a sense, my childhood notion of grace still applies. Like any present offered in love and presented in grand style, grace comes to us free of charge.
But just like any gift that comes in a pretty package, grace is hardly received if we don't open the box and actually make use of it.
Scriptures: Isaiah 55:1-3; John 1:14-17; 14:23; Acts 6:8; 11:23; 13:43; 14:3, 26; 15:11, 40; 18:27; 20:24; Romans 1:5-7; 3:24-26; 5:1-2, 15-21; 6:1-23; 11:5-6; 12:3-8; 15:15-16; 1 Corinthians 1:4-9; 3:10-17; 4:7; 15:10; 2 Corinthians 1:12; 4:15; 6:1-2; 8:1-2; 9:8; 12:9-10; Galatians 1:6, 15; 2:19-21; 5:4, 22-23; Ephesians 1:3-14; 2:4-10; 3:2-12; 4:7; Philippians 1:7; 2 Timothy 1:9; Titus 2:11-14; Hebrews 2:9; 4:16; 13:9; James 4:6; 2 Peter 1:4-10
Books: The Experience and Language of Grace, by Roger Haight, SJ (Paulist Press, 1979)
Idol and Grace: On Transitioning and Subversive Hope, by Orlando O. Espin (Orbis Books, 2014)