who burned cigarette holes in their arms protesting the narcotic tobacco haze of Capitalism,
In order to protest capitalism, and Big Tobacco in particular, they put cigarettes out on their arms.
It's a bit ironic that the speaker praises drug addicts that protest capitalism, yet compares capitalism to a drug ("narcotic tobacco haze").
who distributed Supercommunist pamphlets in Union Square weeping and undressing while the sirens of Los Alamos wailed them down, and wailed down Wall, and the Staten Island ferry also wailed,
Some of the "best minds" are communists. Ginsberg himself was very interested in Marxism, much to the dismay of Jack Kerouac, who refers to him as "Carlo Marx" in On the Road.
They distributed pro-communist pamphlets until they were "wailed down" by police sirens and presumably arrested in places like Los Alamos, New Mexico and Wall Street. It probably didn't help that they were naked after "undressing" in public.
who broke down crying in white gymnasiums naked and trembling before the machinery of other skeletons,
There's that word "machinery" again, this time used in a negative sense relating to skeletons. The "best minds," in fact, may not be more than skeletons after years of starvation or drug use.
The "white gymnasium" sounds like a mental hospital, a homeless shelter, or a refuge.
This section of the poem features a lot of screaming, shrieking, and weeping.
who bit detectives in the neck and shrieked with delight in policecars for committing no crime but their own wild cooking pederasty and intoxication,
It's generally not a good idea to bite police officers, but they did it anyway. Then they got hauled off in the squad car.
Their crimes include "wild cooking," "pederasty," and "intoxication." If "wild cooking" were really a crime, then our grandmother would be in the big house by now.
As for "pederasty," it refers to an erotic relationship between an adult man and an adolescent boy (not as in pedophilia, with pre-adolescent children). This relationship does not necessarily have to be sexual (if it were, it could be an actual crime, depending on the age of the boy). "Pederasty" was common among the Ancient Greeks, for example, including philosophers like Socrates.
who howled on their knees in the subway and were dragged off the roof waving genitals and manuscripts,
They made a commotion on the subway and got kicked off the roof of a building, naked once again.
They are also holding manuscripts, which means they are writers.