The process of approving new projects is highly configurable in Calpendo (see Configuring The Project Approval Process for details). This should be configured in a manner that makes sense for your facility. The basic options are whether to have a single-step or a multi-step approval process.
Single-Step Project Approval Process
A single-step approval process is appropriate when there is a single person who decides whether a project should go ahead, or the decision is made in a single meeting. Under these circumstances, a project changes from its Requested state to either Approved or Denied in a single step. The project's status property is sufficient to handle this, and as far as Calpendo is concerned, the approval process is merely a matter of somebody (probably an administrator) changing the project's status.
An administrator has a choice of how to approve projects using the single-step approval process. The easiest and preferred option is to use The Project Requests Page which shows you just the projects whose status is Requested. It also lets you modify those projects and provides short-cuts to approving or denying new project requests. Alternatively, follow the instructions in Modifying Projects and change the project status as required, or use the Data Explorer to locate the projects to be approved.
There may also be an Automatic Email that tells administrators when there's a project that needs approving. If there is, then the email could include a direct HTML link that will take the administrator to a page with the project already loaded - making approving it very quick.
Restricted projects can only be booked by users with the admin role or by users in a Resource Managers user group (and for the resources they manage only). This is useful for initial testing of the project and pilot studies.
Multi-Step Project Approval Process
A multi-step approval process is appropriate when there are multiple people who must approve each project, and these people make their decisions at different times. To cater for this process, the project should be configured with additional properties to store the information about whether each person has given their approval. The Permissions can be configured to control who can set these approval properties, and even the order in which they must be given. Workflows can be configured to send the next person in the chain an email indicating it's time for them to approve a project. The detail of this process is described in Configuring The Project Approval Process.
This all means that approving a project can mean quite different things, depending on how Calpendo has been configured. However, the multi-step project approval process can always be characterised as some people modifying properties on the project while its status is Requested and then finally somebody changing the project's status to Approved or Denied. This means the project approval process is a matter of all these approvers editing the project in turn, and then somebody edits the project to change its status.
The Project Requests Page is still the preferred way of achieving each of these changes since this page provides a convenient means of locating the requested projects, and the page allows modifications to be made to the projects in exactly the same manner as the other methods, as described by Modifying Projects or using Data Explorer. However, the multi-stage approval process might send Workflows with a nested HTML link directly to the project in question. If that is done, then locating the requested project does not become an issue and so the email could include a link to the List of Projects page or Data Explorer.