Structure of the project
There is very little formal structure to the OpenStreetMap project, and what structure there is reflects the voluntary nature of contributions to the project. There are no super-users who can change the data in ways that "normal" users can't, and there are no fixed ontologies for the data. The data and the project are both intended to give mappers as much flexibility as possible, so they can map features as accurately as they can. While there are system administrators who look after the project's infrastructure, they don't get any more say about what gets put in the database than any other contributor.
The OpenStreetMap Foundation—the non-profit body set up to support the project—doesn't regulate where mappers work, what features they map, or how they describe them. The foundation does have a few working groups that look after various aspects of the project, but they are concerned with long-term development rather than day-to-day operation. The foundation will only intervene when the whole project is being put at risk by the actions of individual mappers.
This relative anarchy is both a strength and weakness of the project. On the positive side, it allows mappers to get on with recording information without needing permission, approval, or moderation. It allows the data to evolve over time to correct mistakes and to take account of changes without the overhead of a top-down design. It allows novel uses of the data without having to check license conditions. However, it also means that problems are addressed according to how interesting they are to individual mappers, rather than how important they may be to the project as a whole, as the volunteers aren't under any obligation to follow a plan.
The project's main website is www.openstreetmap.org, which is aimed at collecting and maintaining the data. Various other websites and resources are used to coordinate the project, including mailing lists, a wiki, a code repository, and an issue tracker. Other tools are also provided by individual mappers or companies, and these have their own websites.
The most important thing to remember is that the project has no paid employees. Even mappers whose job involves working with OpenStreetMap are paid by their companies, who have their own interests, and aren't there to solve other people's problems necessarily. While the OpenStreetMap community will be happy to help you solve any problems you have, you will be expected to make an effort yourself.