Typically a New Patient is created when booking an appointment. However you may also create a new Patient from Clients & Patients. The patient is always linked with a Client. In the case of a New Client, please create a new Client before you create a New Patient.
You can do that from Clients & Patients > New client (green button on right) then fill in the requested information. After this is done, you can call up the new client, and select the +Patient icon to bring you to the Patient page see below.