If you work as a costumer in the theater, a professional theatre or a university costume shop you will almost always be a member of a union. The main union serving North American production specialists is IATSE (International Alliance of Theatrical Stage Employees, Moving Picture Technicians, Artists and Allied Crafts of the United States, Its Territories and Canada) and it has numerous locals broken down by craft including wardrobe, props, hair/makeup, box office ticket sellers and so forth.
If your dream is to be a film costumer the only way you will get hired is by getting a job as an assistant to experienced costumers on a movie or television show that is shooting in your area. This means you will start out in non-union mode and eventually need to qualify for membership. This is usually done by working 30 days for a union company before you can become a member of IATSE.
Once you have qualified as a member of IATSE your life will be much easier. You will have access to a wide range of resources that include information about wages and contracts, studio services, signatory lists, literature, training courses and industry links.
Being a film costumer requires a unique combination of theatricalized character dressing, knowing how things will read on camera (letting you know where you can take short cuts or fake it), logistical expertise in terms of acquiring, tracking, fitting and preparing costumes. Then there is the on-set juggling act of keeping the actors dressed and looking good on camera while not losing valuable shooting time because they have to keep changing clothes. Then there is keeping track of all the various outfits, stunt doubles, photo doubles and dummies that need to be brought on and off the set.