According to the Reformed Tradition (I’m aware that in the RT some diversity exists), upon the exercise of faith, a person is united to Christ by the powerful working of the Spirit. This union with Christ has at least two results. Calvin would note that union with Christ contains a duplex gratia (i.e. double grace). Union with Christ is unpacked, for Calvin, in terms of justification and sanctification. In the RT, these are two distinct and yet inseparable realities. In this post, I offer a simple summary of justification sola fide (i.e. by faith alone).
Having been united to the crucified and resurrected Messiah, two things happen. Thus, another set of two! This time, however, these two things fall under the one heading of justification. First, the believer is forgiven of their sins. Second, the believer is declared righteous in the sight of God. Forgiveness is on the basis of the atoning work of Jesus at the cross where he paid the sinners debt (e.g. Col 2:14). Being declared righteous is on the basis of Jesus’ perfect righteousness imputed to the sinner (e.g. Phil 3:8–9). Thus, by grace through Spirit-wrought faith (cf. Eph 2:8–9), a person stands before God as forgiven and righteous on the ground of the person and work of Jesus Christ (cf. Rom 4:6–8).
In summary, Calvin would write, “Thus we simply explain justification to be: an acceptance by which God receives us into his favor, and esteems us as righteous persons; and we say that it consists in the remission of sins and the imputation of the righteousness of Christ.”
 John Calvin, Justification by Faith, ed. Nate Pickowicz, trans. John Allen, Kindle. (Peterborough, Ontario: H&E Publishing, 2019), loc. 322.