There are multiple routes to follow. I worked as a CBT Therapist for 4 years. The most direct route is to obtain a Masters in Clinical Social Work/Counseling/Psychology. You will want to be sure the program you attend will place you in internships that will focus on CBT training while in school. If the program does not reference Clinical training it most likely will not meet your needs. It is also very important to ensure the program is accredited and nationally recognized.
After completing your Masters you will need to work for a practice/agency/company that will provide you clinical training hours, these requirements differ by state. It takes most 2 or more years to complete these hours. Once you have obtained your clinical training hours you will sit for an exam which will give you a license to practice on you own credentials. You will have to commit to a career of ongoing learning to stay proficient and up to date with best practices.
Burn out from CBT therapy can be high for clinicians - it is important to have a good network of other practitioners to debrief and support each other with difficult cases.