In the United States this is location specific. There is a national rating and membership in the Registry of Interpreters for the Deaf (RID) Their outline of how to become a certified Sign Language Interpreter is at http://www.rid.org/start.html.
In Michigan, where I live, you can attain State Qualification as an alternative to RID certification.
An excerpt from Michigan's code, posted on the Division of Deaf and Hard of Hearing website reads:
"PA 204 was the first step in addressing interpreter quality when persons were not certified. The State Quality Assurance (QA) Screening program was modeled after the national RID's program. The QA program has improved the access for deaf and hard of hearing persons and the quality of interpreting services is better. QA interpreters follow the same code of ethics that nationally certified interpreters do and must obtain continuing education units yearly to keep their qualification level current."
I've known some wonderful Interpreters. In tribute to Brenda Smith, deceased, who was a fabulous interpreter and social worker, I'll repeat the words she gave when someone would ask her how to learn Sign to become an Interpreter:
"Adopt a Deaf person!"
She supported all that schoolwork and books and teachers could do, but sincerely believed that the #1 way to become proficient in Sign was to spend major amounts of time, three or more hours a day everyday, with one or more Deaf persons in situations where only Sign is used.
That's for becoming a Signer, the first step in becoming an Interpreter. Not all Signers are or can be Interpreters. They are different skills. I look for a crossover skill that indicates whether a person is likely to have the brain makeup that allows them to do the act of interpreting. I'll ask them if they like crossword puzzles and can do them with a time clock running. It's a skill that "crosses over" and helps prepare them for the act of interpreting.
Now I'm back editing this to add my belief that it's not necessary to be a Sign Language Interpreter to be of value. In the classroom, the doctor's office, a law office, or across a counter, an Interpreter is still a third person there. How much better to BE the teacher, the doctor, the lawyer or clerk that can function in BOTH English and Sign!
I have many wait-staff as friends and have been asked many times how they can help out their Deaf customers with some common and easy signs: Hi, how are you, do you want (coffee, tea, soda, Coke). Goodbye. Thank you. They tend to love the Sign for Coke!