In wanting to transition from the current hierarchical society to one based on voluntary cooperation without rulership, the question of how to get from "here to there" is one that has been of crucial concern to anarchists of different stripes from day one. However, it's also an issue which has divided them, though they would all at least agree that the strategy of taking state power and strengthening it to bring about libertarian socialism is out of the question. As a consequence, they tend to oppose taking part in electoral politics both on principle and out of the belief that it's ineffective compared to direct action (grassroots activity unmediated by formal political institutions).
However, some anarchists like Noam Chomsky recommend what's called "defensive voting" (using your vote as a form of self-defence against the state) in situations where a certain candidate or party winning an election could be catastrophic, like a fascist coming to power or a war being launched. (For example, he advocated voting for Barack Obama in the 2008 election, though he rightfully advised people not to expect any radical changes. In 2012, he endorsed Green Party candidate Jill Stein). A few others support taking part in municipal elections (though never national elections) so as to devolve the powers of local governments to directly-democratic neighbourhood assemblies and to municipalise enterprises before turning them over to worker self-management, though this is a minority position, with most anarchists being against taking part in any form of electoral politics.
They agree with most other radical socialists that class struggle (of the popular classes against the ruling elites) is a necessary part of social transformation, though they tend to disagree with many, especially Marxists, who see economic class as the only/primary form of oppression, with others - like race, gender, sexuality, nationality, ecology - being secondary or at worst a distraction. Rather, they see it as necessary to integrate class struggle with trans-class forms of struggle, unifying them in a way that makes purely class-based issues (like workplace organising) complement non-economic concerns (like fights against gender or ethnic oppression, or defence of the environment) as part of an intersectional social struggle against all forms of hierarchy and domination, whatever the specific tactics used for achieving an anarchist society.
To offer a brief run down of the various strategies that have been proposed to dissolve hierarchical society and bring about libertarian socialism, they are:
- Insurrection: Armed struggle to violently overthrow the state and private capital and set up a confederation of worker councils and popular assemblies in their place. The tactic of "propaganda by the deed", which was popular in the second half of the 19th century, involved committing small-scale acts of violence against ruling elites in the hope this would incite the working classes to rise up and get into insurrection mode. As the now common image of the Bomb Throwing Anarchist terrorist proves, this didn't work. In fact, it only served to alienate most working people by associating anarchism with mindless terrorism. What few proponents this tactic has today at least agree that they need to get popular support for the uprising before committing any acts of violence, and that isolated acts of terrorism don't do much besides turn people off their cause.
- Anarcho-syndicalism: While many have (somewhat inaccurately) used this term to refer to a social anarchist economic system, it's actually a strategy of achieving libertarian socialism through the use of trade unions. Anarcho-syndicalists propose setting up anarchist syndicates (unions), as well as establishing an anarchist presence in mainstream unions, so as to get as many working people organised as possible and eventually declare a general strike (or "general lock-out of the capitalist classes") to shut down the capitalist economy until the capitalists and landlords agree to sign over control over the means of production, distribution, and investment to the federation of syndicates that would have been established, who would then reorganise the economy on the basis of decentralised worker self-management. This strategy is still very popular today despite having been developed over a century ago in very different economic circumstances. It's also the one that's been most successful thus far, winning many labour victories through trade unions in the early 20th century with the Spanish Revolution of 1936 successfully establishing a libertarian socialist economy for a short time (before being suppressed by Marxists on the Republican side of the Spanish Civil War).
- Dual Power: Creating counter-institutions to capitalism and statism - like worker cooperatives, directly-democratic popular assemblies, affinity groups, democratic schools, interest-free banks, intentional communities - and then linking them all together into a confederated network to contest the power of corporations and governments over the administration of society. Dual Power strategists see this process of "exodus" from hierarchical society as creating an anarchist transfer-culture which will prefigure the forms the new social-institutional structure will take "within the shell of the old". Most want this endeavour to be as nonviolent as possible while still defending the use of self-defensive violence as a last resort to prevent the Dual Power from being dismantled by state or corporate power. It was originally devised by Proudhon and is the primary strategy recommended by market anarchists, though several social anarchists like Gustav Landauer, Paul Goodman, and Murray Bookchin have supported it as well. Some even see Dual Power as compatible with anarcho-syndicalism, with trade unions confronting capital directly (and defending workers from its effects) while the Dual Power institutions try to route around it, offering people an escape from it and from the state.