Let's say you want to change the State (a common target) and you don't want to just pass a law but you want to change the way government works. Or, maybe you want to alter the role of women in the economy, or in Christianity. You might aim to reorient the traditional view of "normal" families as having a father, mother, and children, to include, let's say, same-sex couples or a single-headed households. Sociology suggests many things you can do, and many others that you can only hope for.
Begin by mobilizing resources, recruiting participants, building alliances, and making connections with government elites. As a movement, tell us what's so unjust about the current form of government; convince us that someone - including your social movement - can do something about it; give us a great idea about what should be done about it; give us the sense that "we" belong in this movement; and then get out there and demonstrate it. Keep the public's attention and the authorities on their toes by using disruptive tactics - blockades, boycotts, strikes, sit-ins - particularly tactics that are unfamiliar to authorities and yet easily undertood by your intended audiences. When your tactics no longer create a crisis - i.e., when they become routine for the authorities - move on to a new disruptive tactic. Violence is probably better to avoid, and rather just threaten, unless you think that repression by the State will in your case be a benefit for this movement (this is usually unlikely). Diversify the organization of your movement. Its best to have a mix of centralized, bureaucratic organizations and decentralized, less formalized organizations. Leave the local organizing to the people who know it best - the locals - but nationally coordinate (not necessarily control) and sustain these local centers of organizing. These things are more or less within your control, but there are many important factors that few, if any, control.
Your movement will have more influence on the State if: political elites are divided or realigning their coalitions and alliances; some elites align themselves with your movement to gain political leverage (with the appearance of support from "the people"); repression is at a minimum and/or declining; you can find multiple points of access to the government (multiple decision-making bodies or opportunities to voice your grievances); the government you're targeting has historically treated movements inclusively; and, the government is centralized enough to implement the reforms you seek.
What if it's not the State that you want to change, but religion, or the educational system, the economy, or Science? Most of the above factors still apply, but others may be added. If the institution you're targeting is dependent on "clients," such as, customers, investors, benefactors, or others that consume its services, then it's more vulnerable to your movement. If it is tied to the State (e.g., maybe it receives money from the State, or the State is a major client), then you might find opportunities for alliances with other movements that are targeting the state. Institutions are also more vulnerable when they experience rapid growth in members, money, and/or organizations, and have a decentralized power structure.
A successful social movement to change institutions is likely to be one that can mobilize resources and skillfully employ them in creative and effective ways. However, even those movements that do this may not be successful. The state of the institutions you take on also matters, being more or less vulnerable to your challenge. Some institutional factors mentioned above are unlikely to change at all, but others may rise and fall as economic, political, and social conditions change. It is during these fleeting times of institutional vulnerability that your movement has a window of opportunity to change the institution, if it's already organized to take advantage of it.