You can add a new project by either going to Projects → Add project or to Clients → select a client → Projects → New project.
By default, only admin users can add projects. Project managers and regular users can add projects as well, only if one of the admins grants them this privilege by going to Users → select the user → Edit → Privileges and checking the “Can add projects” option.
Watch this video to see in more detail how you can create your first project.