Some permits, like Building Permits, are ministerial. These have specific standards defined in the zoning code. If your project meets all these standards, it gets approved. These approvals are done by County staff and in some cases can even be done over the counter.
Other permits, like Use Permits, are discretionary. These require someone (often the Planning Commission) to make a determination on whether certain findings can be made that the project supports the County's overall goals, based on the facts of that individual case. When you apply for one of these permits, County staff will review it, refer it out for comments by other agencies and groups, and prepare a Staff Report recommending approval or denial. These Staff Reports, and most comments and materials that inform them, are public records, and may be accessed by anyone for any project upon request. Recent ones are also posted on the County website. Once a Staff Report has been prepared, a public hearing is usually held where Staff presents their recommendation to the deciding body and the applicant has time to present as well. There is also a public comment period, where any member of the public can raise concerns or speak in support of the project, either by submitting written comment or speaking at the hearing itself.
Once all comments and material has been heard, the deciding body publicly deliberates and makes its decision on whether to approve the project. Approvals of discretionary permits often come with conditions to ensure environmental protection, community safety, or other goals of development in the County.