Different states have different requirements to inject Botox. Most Plastic Surgeons get experience in this during their extensive training process. Training programs are offered to allow additional information and improve the experience. Allergan (the manufacturer of Botox) has several physician trainers that are able to provide education to other practioners in their area.
Training to be able to inject botox can be achieved in many ways. Doing a plastic surgery residency or fellowship, going to a course sponsored by the company, becoming an aesthetician, etc. There are many ways to go about it, but I would make sure that the person who is injecting you is experienced and is under the supervision of a plastic surgeon.