As I understand it, anarchism is less about eliminating laws and more about eliminating hierarchy. It's bottom-up governance that requires lots of participation from everyone involved. You and your peers can establish laws for your neighborhood/town/etc., but everyone affected by that law needs to directly participate in its writing and there must be broad consensus before it is enacted. Law enforcement must be communal; you cannot outsource it to a police force, lest the police become oppressive.

When I think of anarchism I sometimes think of colonial New England: small towns that are largely autonomous, where communal decisions are made at town hall meetings and the locals manage themselves. It's not a perfect analogy since there were higher levels of government, but day-to-day governance was very grass-roots.