Simply put, any atom attached to a chiral carbon has higher Cahn-Ingold-Prelog priority corresponding to its atomic number--the higher the atomic number, the higher the priority.
If two atoms attached to the chiral center have the same atomic number, then the sum of the atomic numbers of the atoms one bond further from the chiral center are totalled, and so on progressing out from the chiral center until one branch or the other originating at the chiral center is found to have higher priority. (If no such difference is found, then the carbon in question is not, indeed, a site of chirality)