http://anarchy101.org/25/why-does-capitalism-rely-on-the-state
that addresses the connection between capitalism and coercive, hierarchical relations and violence.
as for how anarchists fight it... that's a huge question, obviously.
some people attempt to fight it by organizing (or educating) people - who theoretically have the power, in large enough numbers, to operate in some way that is not capitalist, or to end capitalism.
other people leave social arenas where capitalism (qua buying and selling) is more obvious - but constraining capitalism to money interactions is an incredible simplification.
other people emphasize the importance of relationships, and doing things with and for their friends - again, without money. again, money is to capitalism as the police force is to the state: merely the obvious scapegoat.
other people attempt to destroy the things around them that are what capitalism rests on (property, certain social relations, etc).
some people do all of the above, maybe.
