How to obtain coordinates of points in new coordinate system?

If I know the positions of all points (3D) and its origin is (0,0,0), but after shifting the three axes, the point (a,b,c) in the old system will be set as the origin (0,0,0) in the new system. Then how to calculate all other points' coordinates in the new system?

[Walter Roberson]

What is the order of transformations? Are you rotating around the original (0,0,0) and then translating resulting point (a,b,c) to be at (0,0,0) ? Or are you translating (a,b,c) to be at (0,0,0) and then rotating around that new (0,0,0) ?