When someone commits a motor vehicle offense in New Jersey they are typically cited by the means of a ticket and scheduled for a hearing in municipal court. You should contact the NJ Motor Vehicle Commission or the court, which your citation should list, to find out if you bring in your valid NJ driver's license if the violation will be dismissed.
Usually it is not dismissed if you did not have it at the time of infraction, but some judges courts will offer leniency based upon the situation.
The ticket amount should be listed on the back of the ticket. In some cases there might be a fine or court fees to go along with this or you might have to wait for your court date to appear.
To find out the exact amount of the fine or court fees that might be associated with this offense, again ask the NJ MVC or court house. Auto insurance rates for New Jersey are available starting here.