To do something extra or different to work in orthodontics?

As an orthodontist? The other advisors have provided excellent advise; however, if you are asking what is required to a dental specialist, orthodontist, then the answer is completion of dental school followed by a 2-3 year accredited residency training. Limiting one's practice to a speciality may also require specific licensing in the state where you practice as well.
Yes you do. Depending on what job you have in the orthodontic office, there is special training and experience needed. The amount of extra training and schools needed depends on the job, the orthodontist, the orthodontic assistants, and the support office team. All need some or extensive schooling or training.
In what position? An orthodontic office includes but not limited to a scheduling coordinator, financial coordinator, insurance coordinator, orthodontic dental assistant, orthodontist, office manager, and sometimes a dental hygienist. Some ortho offices have employees doing more than just one task though. And some offices have multiple people in each position. An orthodontist is a dental specialist.
Ortho Assistant. The best way to "learn" how to work in an orthodontic office is to learn in a program that specialized in training dental assistants. Once out, in a good orthodontic office, the orthodontist will in fact further train you to his/her specifics/needs in the office.
Maybe not. if your state offers a dental assisting program then it may be required by law to take and pass program before employment . discuss options with a local orthodontist and he can guide you.
Training. Usually you need to go to a dental assisting school to get the basics but then you will need further training later on by an orthodontist. Another option would be to volunteer at an orthodontic office and really bust butt and prove yourself so they know you would be an excellent employee and they would probably hire you and train you.
Training. While all Dentist's can provide Orthodontic care, to be an Orthodontic Specialist requires 2-3+ years (2,000+hrs/year) supervised Residency training. To work in an auxiliary capacity as an Orthodintic assistant, a Hygienist in an Orthodontic practice, a receptionist, treatment coordinator, or any other position requires training in an educational setting or in an office setting.
Training. As an assistant, you need to be trained to assist with orthodontics. To be an orthodontist, you need to complete an orthodontic residency program.