The hoary phrase "right to work" has been appearing frequently in news reporting on the efforts by many Republican governors to weaken the power of public sector workers. This phrase, while very useful for opponents of unions, fundamentally misrepresents what is at issue.
There are absolutely no circumstances in which someone is denied the "right to work" in the absence of the laws that go under this name. These laws are actually about restricting the freedom of contract. Under U.S. labor law, unions are required to represent all the workers in a bargaining unit that they represent, regardless of whether or not they belong to the union.
This means that workers who opt not to join a union still benefit from the union's representation. This is true both in the sense that non-members get the same contract that union members receive (the contract can't specify one wage scale for union members and another for non-members) and also the union is required to defend the rights guaranteed to non-members on the contract. For example, if a non-member is fired or in any other way sanctioned, the union is required under the law to defend their rights as described in the contract.
In other words, U.S. labor law requires that the union incur costs to represent workers in a bargaining unit whether or not they choose to join the union. Not surprisingly, unions like to sign contracts that require workers to pay for this representation. This is a condition of employment just like employers impose conditions of employment (you don't like the pay, go work somewhere else).
So called "right to work" laws prohibit unions and employers from signing contracts that require workers to pay for their union representation. In this sense they could more accurately be termed "right to freeload," since they guarantee that workers will have the opportunity to benefit from union representation without paying for it.