To obtain a moped permit in New Jersey, you must be at least 15 years old, complete an application for a moped permit at a motor vehicle agency, fulfill the 6 Points of ID requirements, pass the knowledge and vision tests, practice riding with your permit for a minimum of 20 days, and pass the road test to receive your moped license. It's essential to adhere to the state's requirements and obtain the necessary permit to legally operate a moped in New Jersey.