This is more complicated than you might expect, since Catholicism and Protestantism (which often takes a "salvation by grace alone" approach) can have slightly different approaches to concepts like justification, salvation, faith, grace, and merit.
In Catholic belief, salvation is achieved not in an instant, nor by predestination before birth, but over a lifetime. Ultimately justification, which is "not only the remission of sins, but also the sanctification and renewal of the interior man"1, is a gift of the Holy Spirit:
The grace of the Holy Spirit has the power to justify us, that is, to cleanse us from our sins and to communicate to us "the righteousness of God through faith in Jesus Christ" and through Baptism.
(Catechism of the Catholic Church, paragraph 1987, quoting Romans 3:22)
Justification is not merited by the works of any human being, but by the death of Christ, and is granted to the believer at Baptism, "the gateway to the Sacraments":
Justification has been merited for us by the Passion of Christ who offered himself on the cross as a living victim, holy and pleasing to God, and whose blood has become the instrument of atonement for the sins of all men. Justification is conferred in Baptism, the sacrament of faith. It conforms us to the righteousness of God, who makes us inwardly just by the power of his mercy. Its purpose is the glory of God and of Christ, and the gift of eternal life.
(Catechism, paragraph 1992)
Justification, however, does not ensure our salvation. Justification enables us to cooperate with the saving grace of God; but if humans do not cooperate with His grace, they will fall away from His love and may in the end come to reject him.
According to the Catechism of the Catholic Church, "we cannot ... rely on our feelings or our works to conclude that we are justified and saved. ... reflection on God’s blessings in our life and in the lives of the saints offers us a guarantee that grace is at work in us" (paragraph 2005).
Works—that is, the good things that we do, impelled and strengthened by God's grace—do have a place in our salvation; but it is not precisely correct to say that "we are saved by works":
The merit of man before God in the Christian life arises from the fact that God has freely chosen to associate man with the work of his grace. The fatherly action of God is first on his own initiative, and then follows man’s free acting through his collaboration, so that the merit of good works is to be attributed in the first place to the grace of God, then to the faithful. Man’s merit, moreover, itself is due to God, for his good actions proceed in Christ, from the predispositions and assistance given by the Holy Spirit.
Since the initiative belongs to God in the order of grace, no one can merit the initial grace of forgiveness and justification, at the beginning of conversion. Moved by the Holy Spirit and by charity, we can then merit for ourselves and for others the graces needed for our sanctification, for the increase of grace and charity, and for the attainment of eternal life.
The charity of Christ is the source in us of all our merits before God.
(Catechism, paragraph 2008, 2009, 2010; emphasis in bold added)
Thus, the belief of the Catholic Church is that neither "salvation by grace alone" nor "salvation by works" is true in itself; rather, salvation begins when God gives us His grace, which allows us, through His Son's love, to come to merit further graces and sanctification, and ends when, at the end of our lives, we can accept his offer of life with Him in heaven. The Catechism quotes St. Thérèse of Lisieux:
After earth’s exile, I hope to go and enjoy you in the fatherland, but I do not want to lay up merits for heaven. I want to work for your love alone.... In the evening of this life, I shall appear before you with empty hands, for I do not ask you, Lord, to count my works. All our justice is blemished in your eyes. I wish, then, to be clothed in your own justice and to receive from your love the eternal possession of yourself.
As far as what your friends are saying, each of them is correct in a sense, but incomplete. Surely it is grace, as I said above, which ultimately renews and sanctifies us, and which gives us the ability to merit salvation; but as I mention it is not entirely correct, or at least not entirely complete, to assert that "salvation is by grace alone". We must cooperate with God's grace.
On the other hand, following the Ten Commandments—the "Old Law"—is not complete in itself, either. Jesus has given us much more.
According to Christian tradition, the Law is holy, spiritual, and good, yet still imperfect. Like a tutor it shows what must be done, but does not of itself give the strength, the grace of the Spirit, to fulfill it. Because of sin, which it cannot remove, it remains a law of bondage. According to St. Paul, its special function is to denounce and disclose sin, which constitutes a "law of concupiscence" in the human heart. However, the Law remains the first stage on the way to the kingdom. It prepares and disposes the chosen people and each Christian for conversion and faith in the Savior God. It provides a teaching which endures for ever, like the Word of God.
The New Law is the grace of the Holy Spirit given to the faithful through faith in Christ. It works through charity; it uses the Sermon on the Mount to teach us what must be done and makes use of the sacraments to give us the grace to do it.
(Catechism, paragraphs 1963, 1966)
1 Council of Trent, cited in Catechism of the Catholic Church paragraph 1989.
