How are we justified through faith alone?  

Peter Jeffrey:  in Giving His Son to die in our place God demonstrated His Justice.  Our sins are not overlooked.  They are dealt with exactly as God had always said they should be dealt with.  They are punished, but because they have been laid on Jesus and he has taken responsibility for them, he takes our punishment instead of us. On the Grounds of what Jesus has done, God is able to justify guilty sinners.  He is acting in a perfectly lawful way because our sins have been dealt with according to divine law.  Our sins are credited to Jesus and God treats Jesus as he should treat us–he is forsaken and dies in our place.  Jesus righteousness is credited to us and God treats us as he has always treated Jesus–we become his children and he owns us as his redeemed people.  

CJ Mahaney Faith is not a means of saving ourselves; faith/repentance is a means of admitting we cannot save ourselves. It is a way of throwing ourselves upon the mercy of God and begging the savior to save us.  

Martin Lloyd Jones: It does not mean we are made righteous, but rather that God regards us as righteous and declares us to be righteous.  This has often been a difficulty to many people.  They say that because they are conscious of sin within they cannot be in a justified state; but anyone who speaks like that shows immediately that he has not understanding of this great and crucial doctrine of justification. Justification makes no actual change in us; but is a declaration by God concerning us.  It is not something that results from what we do but rather something that is done for us.  We have only been made righteous in the sense that God regard us to as righteous, and pronounces us to be righteous.