Gene therapy is where diseases are treated by altering the genes of the affected person, by fixing or replacing the faulty genes. In most/all gene therapy processes, non-faulty DNA is inserted into a vector which then inserts the DNA into the cells affected through 'transfection'. So for instance, we could take a virus, liposome or some other molecular transporter (let's just go with a virus for now), replace its genetic material with the non-faulty DNA and allow it to infect a sample of cells taken from the patient. The DNA is taken by the virus into the cell, where it is placed into the existing genetic material once the virus reaches the cell nucleus. Thus the corrected DNA is integrated with the patient's DNA. Then, the cells are cultured, so that we have amplified the correct gene. Finally, we introduce the cells to the patient, who will be temporarily relieved of the disease.
NB. The process has to be repeated regularly for relief to be sustained. However, using stem cells to amplify the gene is apparently better, as it provides longer lasting relief.
Hope this helped!