How did labor unions win the support of workers?
By directly benefiting working people through better wages and working conditions. When workers see direct benefits they want to join in. Unions provided political action to change laws.
The Industrial Revolution increased the urban workforce. Machines could work 24 hours a day but they still needed people to make them work properly. Organized labor could band people together and affect the finances of companies by strike action. With the support of Governments and laws for fair dealing they were able to negotiate to get contracts for wage and working condition improvements. Unions could balance the power of the capitalists.