Typically, projects are created during their first analysis and never deleted (because old software never dies). For atypical situations, there is the page at Administration > Projects > Management, which allows you to manage project existence.
Provisioning a project allows you to declare and configure it (define permissions, set quality profiles, etc.) before running the first analysis. To be able to provision projects, you have to be logged in and be granted the Provision Projects permission.
To provision a new project, go to Administration > Projects > Management and click on Create Project. The only required information is the key and the name of your project.
Once the project is provisioned, you can configure it (define permissions, set quality profiles, etc.), and when you're finished with the configuration, you can simply run the project's first analysis.
You can also provision and configure projects using the Web API.
Projects may be deleted individually from the project pages themselves. See Project Administration for more. To delete projects en masse, use Administration > Projects > Management. Here you can select the projects to delete.
Note that the "Select all" checkbox selects all visible projects in the list. By default, only the first 50 projects are shown. Projects can be added to the list in sets of 50. If "select all" has been used, projects added to the list will not be pre-selected.
Projects where analysis has been attempted but never succeeded are "Ghosts". Ghosts can be safely deleted from the Ghosts view.