The just shall live by faith. This is a quote from Habakuk that occurs in Romans, Galatians and Hebrews. In Romans the Apostle Paul uses this to show the individual how to get saved, by faith. In Galatians though the Apostle Paul uses it to show the Galatians that their continued walk with God was not to be by works of the law but by faith in the finished work of Christ. The Christian is to proceed in his faith the same way he entered into it, by faith.
The Apostle Paul in Romans chapter 6, discusses the process of sanctification using three terms: know, reckon, and yield. We are to know that Christ by his work on the cross has defeated sin's power over us. We are to reckon that this is true of us and we are to yield ourselves to this. I can live the christian life by trusting that Christ will give me the power to do so.
The best illustration of 'the just shall live by faith' for both salvation and sanctification is when Peter walked on the water. He knew that Christ had commanded him to walk out to him. He reckoned that Christ's command made it possible and he yielded to it by stepping out trusting that Christ's power would enable him to fulfill his lord's command.
Sadly, we also see in this story why the regenerate christian fails. When Peter ceased to focus on Christ and instead became worried about the conditions around him, he began to sink. Christians fail because they put their reliance on the things of the world rather than Christ.
Just as walking on water is impossible by our own power so too is it impossible to live the christian life without faith in Christ.
This is just like someone trying to sober up. First you got to admit you have a problem (sin). Then you have to admit that you need help (Christ). Then you have to make the change in your life (change your ways). Then the spirit of Christ cleanses you. A baptism to cleans from sins is also part of this.