You have to be registered with the government as a voter in order to vote at all. When you register, you list your party affiliation. If it is one of the major parties, that information also adds you to the party's list of members, granting you the ability to vote in their primary elections. If you register as an independent (e.g. unaffiliated) voter, it depends on what state you're in, but sometimes you can vote in either primary and sometimes none at all. Note that there is also an Independent Party, which is different from lowercase independent, meaning no party affiliation at all.