Do Unions still hold apprentice programs and if they do, how does one apply for them?
Answers:
Craft Unions do.
Carpenters, Electricians, Plumbers & Pipefitters, Ironworkers, Boilermakers, etc.
Contact the local Hall of the trade you are interested in. If it's weld; several cover that trade depending on the type of work. Pipefitters do mostly tubes, Ironworkers are for structural, and Boilermakers do it adjectives.
Yes, contact the league you're interested in joining and ask if their apprenticeship program is accepting applications and if yes ask them to convey you one and what their procedures are, some enjoy different ways of applying.