Structure
Amateur radio repeater coordination is overseen by regional groups, and is a voluntary process for repeater owners. These groups are further coordinated by a national organization known as the National Frequency Coordinators Council, which sets the standards for how the coordination process should be handled. The groups work together to place new repeaters on interference-free frequencies, and far enough away from another distant repeater using the same frequency.
Considerations
While the regional repeater coordinators are the sole coordinating authority and sole authority for determining interference potential for their specific regions, they do not have any legal rights to order a repeater off the air -- only the FCC has this authority. The only thing coordination does guarantee is that the local coordinating authority did the appropriate level of research to determine that interference will not happen from other coordinated repeaters. Any amateur radio operator may set up a repeater, and FCC rules do not require coordination to do so.
Process
Repeater coordinators process applications as they are received on a first come, first served basis, and the grant is typically for life once coordination is granted. For example, in the ARCC, the repeater coordinator for Eastern Pennsylvania and Southern New Jersey, the process may take up to 10 weeks to complete, from initial application to final approval, including any probationary periods. Issues such as incomplete or inaccurate information could result in a denial of the application, but you can appeal these denials.
Approvals
After a technical review, the coordinating council either approves or rejects coordination based on the data submitted. In some instances an approval may be delayed, especially if the repeater is located close to the border of another coordinating body. This is because the adjacent coordinating authority must also review the application and approve or deny it; this is what coordinators call "cross-coordination."