I should preface this answer by pointing out that Catholics and non-Catholic Christians may not mean the same thing at all when they each say the word "faith". When a Catholic says "faith" in a context like this, he means free assent to the whole truth that God has revealed (CCC 150). This is not a complete definition of faith but it's an essential part. I'm not sure that it coincides with a typical non-Catholic understanding of the fides in sola fides.
At any rate the other answers so far are helpful in distinguishing between faith and works generally, but it sounds like the original question is focused more on the distinction between faith and grace.
Your question seems to hinge on one particular aspect of Catholic doctrine:
God gives us grace to perform the meritorious works that earn our salvation.
Strictly speaking this is an accurate statement from the Catholic viewpoint; cf. for example the Catholic Catechism on "Merit" (emphasis in original):
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
But this is is a difficult and somewhat mysterious concept, because anyone who is able to perform "meritorious works" of this sort is by definition already justified (in more typically Catholic language, is already in a state of sanctifying grace).
Or, to put it more succinctly: only the just are able to perform meritorious works. So in one sense there is no question of earning one's salvation by meritorious works.
On the other hand the Church teaches very clearly, as quoted above, that the just can "merit ... the attainment of eternal life". What this means precisely (to the extent that it can be understood at all) might best be explored in a separate question.
And all of that still leaves the question "how is one justified?" (Catholic translation: how does one attain a state of sanctifying grace?). The simple, externally visible answer in the normal course of most people's lives is "by being baptized".
But that's not a complete answer by any means, because the Church teaches that there is a lot going on within the believer prior to baptism, and that after baptism one could in fact lose one's justification (Catholic translation: sin mortally) and would then need to be justified again (be restored to sanctifying grace), which God normally achieves in the context of sacramental confession.
In any event, the supernatural virtue of faith, which is a gift from God, is foundational to the process of justification, but in typically careful fashion the Church notes that faith is a virtue of the intellect, whereas the will must also be prepared for justification. From the Catholic Encyclopedia entry on "Sanctifying Grace":
The Council of Trent (Sess. VI, can. ix) decrees that over and above
the faith which formally dwells in the intellect, other acts of
predisposition, arising from the will, such as fear, hope, love,
contrition, and good resolution (loc. cit., cap. vi), are necessary
for the reception of the grace of justification.
How then do we read Romans 3 & 4? I'm not sure if there's an official Catholic answer to that, but it does seem that any interpretation must also be compatible with, on the one hand, the 'work' of Philippians 2:12 and the 'crown ... which the Lord ... will award' of 2 Timothy 4:7-8 -- not to mention the necessity of baptism* as expressed in John 3:5.
*Bearing in mind that besides sacramental baptism there is also the baptism of blood and the baptism of desire