29 CFR 1910.134 requires employers to provide "effective" training to employees who are required to use respirators. This training must be completed before the worker uses a respirator, and must reoccur at least annually.
The regulation does not list any specific requirements for trainer qualifications. It just says that it must be "effective", and provided in a manner that is understandable to the employee. It is always good practice to designate someone who has knowledge, training, and experience on the hazards of the workplace and respirator use. It's also a good idea to make your designation in writing.
Video: Respiratory Protection Training Requirements