Start on the Contact Detail page (by clicking on any contact name from a project, or the client list). In the middle of the page you will see CONTACTS. There is an ADD CONTACT link.
Click that link and you will see the overlay where you can add a new contact, along with all their information and even an optional photo for fast recognition.
You can add as many contacts to a client as you like. You can also EDIT the contact by clicking their name in the list.