Anarchism is commonly understood as opposition to hierarchy, the vertical ordering of people on the basis of power. How this opposition can be demonstrated is not an easy question, however, insofar as participating in hierarchies of one form or another is unavoidable for most people in modern societies. How this opposition can be broadened can seem even more perplexing.
Many anarchists are good at reducing their exposure to hierarchies on an individual level; for example, by participating in small-scale cooperative activities. Such efforts are meant to perform a dual function: they provide individuals the experience of working without hierarchy, and they serve as examples to the rest of society that such alternatives exist.
Unfortunately, small-scale cooperatives are themselves at a power disadvantage in relation to state capitalist institutions, and frequently fail or fail to grow past a certain point. What is doubly unfortunate is when the anarchists involved become culturally alienated from working class people in "mainstream" society, and fail to do the kind of outreach necessary to keep their projects growing in scale.
There is a particular need for anarchists who can do effective propaganda both from within and external to functioning anarchist organizations. This means promoting anarchist practices inside hierarchical organizations, where most of humanity already is anyways.
Practicing anarchism inside or between hierarchies may sound like an impossibility, but not if we apply the same principles we observe in the circumstances we can control to the circumstances we mostly can't. This would mean identifying those parts of a particular hierarchy which do and do not have social legitimacy, and picking our targets accordingly: some to promote and some to oppose.
How do we know what is socially legitimate within an institution which, at its core, has no intrinsic legitimacy? The answer is: they are the practices, policies, and other norms that people would likely support, or which our principles endorse, under non-hierarchical conditions.
This can include things like women's equality in the workplace, equal opportunity employment, ending Don't Ask, Don't Tell; and other institutional practices that are socially justified regardless of the circumstances. Such reforms can be used to support people within hierarchies while showcasing the anarchist principle that how organizations are constituted at present is not necessarily how they need to remain, once exposed to the light of human preferences.
Supporting what is socially justified internal to particular hierarchies is probably the only way we have to directly communicate anarchist principles to the people confined within them; what anarchists accomplish without a direct line of communication to their intended audience is almost never fully understood. It is also probably the only realistic way for most anarchists to actually practice their principles, without inviting the problem of leaving society altogether.