The Gay movement can be mapped as the classic case of moving from private to public. Before the movement, intimate love for another of the same sex was said to be "in the closet." It was kept as private as possible. Gay people had to develop rituals to "find others." Society has many rituals through which male-female relationships can develop toward love and intimacy. But similar rituals for gays were lacking. They would have be "deviant." So, those Gays had to negotiate such rituals carefully so as not to stimilate the retribution of a normative society. In the process they would gradually carve out public spaces where they could meet similar others. The process of moving to these as public (a community of shared concerns) was the direction of the movement.
Toward this end, there were scattered demonstrations in the 1960s. They tended to be only in certain cities: Philadelphia, San Francisco, New York, Washington. They were within the context of the radicalism of the decade and the pattern of mass rallies characteristic of many movements.
One of the events that is pointed to by many as the start of the Gay movement is the Stonewall Riot of 1969. One important public sphere for gays had become the gay bar, establishments, generally in large cities, where gay behaviors were accepted by management. The governments of these cities tended to go through cycles of (1) letting these places operate as gay bars; they were, after all, private businesses; (2) moving into pressure from public and governmental officials for the police to do something about them; and then (3) raids, often vicious, in which police tended to have license to punish patrons on the spot, either through arrest citing various sodomy statutes, or through violence. On 28 June 1969, at the Stonewall Inn in Greenwich Village of New York, the third stage was reached. But the patrons resisted the police efforts. It became a symbol of oppression against gays.
Other than New York, the most active central location for the movement (that was, remember, very decentralized) was San Francisco. Many radical movements of the 1960s prospered in San Francisco and the Gay movement was no different. The Vanguard Movement was organized there in 1965, and then a community of gays formed around the Castro District of San Francisco. This community had an economic and political energy as well as an energy toward positive identity. Members developed businesses catering to other gays, but to ordinary citizens as well. And the community began to get involved in San Francisco city politics and even state politics. The community became a magnet attracting more and more activism.
Generally the gay movment was very dispersed. Small cohorts formed the public spheres that supported each other in the face of the weight of normativity. This was bottom-up. Generally no leadership.
Beyond that, groups began to form locally. For example, the Vanguard formed in San Francisco as a community support organization in 1965.