When creating a new project, you'll be presented a pop-up window. In here, you'll be able to name the project and add a customer. To add a customer, start typing in the "Add Customers and Teams" box.
If the name exists in your contacts section, it will be in the drop down list. Select someone to add them as a customer. If they don't exist in the contacts section, you'll be asked to press the Enter key and create a new contact on the fly.