A labor union is an organization formed by workers who come together to improve their working conditions through collective action. By pooling their individual strength, workers can negotiate with employers as a united front, making it more difficult for bosses to take advantage of them.
In essence, companies don't need any one worker, but they do need all of them.
Many of the benefits we enjoy today are thanks to the collective efforts of labor unions, such as:
The vast majority of American workers have the legal right to form or join a labor union.
The only groups that definitely can't are managers, supervisors, and close family of a company's owners.
Unfortunately, the following groups may or may not be protected based on state laws: independent contractors, agricultural laborers, domestic workers, religious institution workers, and local/state government employees.
Everyone else has the legal right to form or join a labor union.
The vast majority of American workers have the legal right to form or join a labor union. So almost anyone can start the process. Here's what it looks like:
Employees decide on a bargaining unit, such as their entire workplace or specific departments, and start organizing support for their union among workers in that unit. While momentum is building, organizing is typically kept secret from the boss to avoid retaliation and to delay the company from hiring union busters to oppose the effort.
Once 30% of employees in the bargaining unit indicate that they support their union, they can request their union certification election through the National Labor Relations Board (NLRB). However, it's recommended to wait for an 80% supermajority of support instead. That's because once the election is requested, bosses are notified, so the effort is no longer secret. At that point bosses typically hire union busters who can decrease support by 20% or more.
The NLRB typically sets the vote on a date within one month of the request. However, the vote can be delayed if the company legally challenges the bargaining unit definition.
Every employee in the bargaining unit receives a secret ballot from the NLRB. Then, on the day of the vote, the NLRB counts up all the ballots that employees returned. If more than 50% are "yes" votes, the NLRB certifies the employees' union.
Finally negotiations with management begin, where employees can secure real workplace improvements with a union contract for years to come.
For more info, see the NLRB page on how they Conduct Elections.