My orientation to these questions comes from experience in the Vietnam antiwar movement, which I consider a model for Marxist participation in the mass movement. The goal of the movement was withdrawal of American troops. As the mass movement grew, the opportunities for developing socialist consciousness also grew. I myself became a Marxist in the course of discussing antiwar politics with people at the New School in 1967.
Of course, the antiwar movement had the specific character that it did because some of the key leaders were CIO veterans. I would single out AJ Muste first and foremost, who was a Trotskyist in the 1930s and led the Toledo Autolite strike. When he got involved in the antiwar movement, he had evolved into a radical pacifist but was clear on the class question: the US had no right to be in Vietnam. I also include Gil Green of the Communist Party, a great leader. And finally I include Fred Halstead of the SWP. He wrote a chronicle of the antiwar movement called "Out Now" that I highly recommend. Fred was a rank-and-file participant in the "Bring us Home" movement in 1945, when American soldiers in the Pacific theater protested against the move to use them against Mao. Many of the organizers of the movement were GI's who had been CIO trade union militants. Fred's major contribution to the antiwar movement was to make the point that American GI's were working-class victims of imperialism, and not killers. This meant that the antiwar movement eschewed Spart slogans like "Drive the GI's into the Sea!" Eventually this strategy paid off as thousands of active-duty GI's, including many in Indochina itself, began to protest the war.
Louis Proyect
(http://www.panix.com/~lnp3/marxism.html)