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The Catholic Church teaches that good works done after regeneration (at baptism) and justification are (if certain conditions are met) meritorious and can contribute to salvation and attainment of eternal life, but only hand-in-hand with, soaked in, enabled by, grace, which alone saves us. Catholics believe in sola gratia.
But it is a faith that is not separated from works (per James). Faith inherently includes these works. We’re not saved by faith alone (that’s where Protestantism errs); we’re saved by grace alone.
We may describe Catholic soteriology as follows:
By the grace of God, we are saved through our faith; this faith entails by its very nature, good works, always enabled by prior grace, without which it is dead.
These are the necessary distinctions we must make, so as not to be miscategorized as Pelagians or semi-Pelagians (historic heresies – condemned by the Church – which held that one could be saved by works without necessary preceding grace). Grace enables all faith and meritorious good works, which are all part of the package of justification / sanctification and eventual final salvation.
Grace is primary in the whole process, so in that very real sense we can describe our system as “saved by grace alone” — whereas we can never say “saved by faith alone” (i.e., with works playing no part at all in salvation) or “saved by works alone”.
The true Catholic position will always include the works alongside grace and faith. We teach neither sola Scriptura, nor sola ecclesia, nor sola traditio.
Pope Benedict XVI stated in a General Audience (8 November 2006): “it is to him and his grace alone that we owe what we are as Christians.” He observed again in a homily on 25 January 2008: “The awareness that divine grace alone could bring about such a conversion never left Paul.”
Here are some scriptural passages that highlight grace in justification and salvation:
Acts 15:11 (RSV). . . we shall be saved through the grace of the Lord Jesus, . . .
Acts 18:27 . . . When he arrived, he greatly helped those who through grace had believed.
Acts 20:24, 32 . . . the gospel of the grace of God.. . . And now I commend you to God and to the word of his grace, which is able to build you up and to give you the inheritance among all those who are sanctified.
Romans 3:24 they are justified by his grace as a gift, through the redemption which is in Christ Jesus,
Romans 5:15, 17 But the free gift is not like the trespass. For if many died through one man’s trespass, much more have the grace of God and the free gift in the grace of that one man Jesus Christ abounded for many. . . . If, because of one man’s trespass, death reigned through that one man, much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ. (cf. 5:2; 6:14)
Romans 11:5-6 So too at the present time there is a remnant, chosen by grace. But if it is by grace, it is no longer on the basis of works; otherwise grace would no longer be grace.
Ephesians 2:9-10 For by grace you have been saved through faith; and this is not your own doing, it is the gift of God — not because of works, lest any man should boast. For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them. (cf. 1:7)
2 Timothy 1:9 who saved us and called us with a holy calling, not in virtue of our works but in virtue of his own purpose and the grace which he gave us in Christ Jesus ages ago,
Titus 3:7 so that we might be justified by his grace and become heirs in hope of eternal life. (cf. 2:11)
1 Peter 1:10 The prophets who prophesied of the grace that was to be yours searched and inquired about this salvation;
Note, then, the overwhelming usage of grace as tied to salvation, or to the justification that will lead to salvation if a person perseveres to the end (including doing good and meritorious works). Salvation is undeniably tied in explicitly with grace in four passages above (Acts 15:11; Eph 2:9-10; 2 Tim 1:9; 1 Pet 1:10; cf. also Titus 2:11), and two of them (Eph 2:8-9; 2 Tim 1:9) explicitly deny salvation by works.
The error of faith alone is also expressly denied:
James 2:14, 17-18, 20, 22, 24, 26 What does it profit, my brethren, if a man says he has faith but has not works? Can his faith save him? . . .  So faith by itself, if it has no works, is dead.  But some one will say, “You have faith and I have works.” Show me your faith apart from your works, and I by my works will show you my faith. . . .  Do you want to be shown, you shallow man, that faith apart from works is barren? . . .  You see that faith was active along with his works, and faith was completed by works, . . .  You see that a man is justified by works and not by faith alone. . . .  For as the body apart from the spirit is dead, so faith apart from works is dead.
We see above, directly in 2:24 and indirectly in all the others, that works play a part in the sanctification and salvation process. The two passages in this overall context that teach “justification by works” (2:21, 25) have to be interpreted in light of the surrounding passages (works not being isolated in terms of salvific power, but only relevant insofar as they are intertwined with faith produced by God’s grace). Works and faith are tied together in grace.