When you add a Contact Form to a project, it means that when you are creating a new contact, you can choose this Contact Form as the one that will be filled in when creating the contact.
Steps
Go to the Project Preferences page of the project that you want to add the Contact Form to
You can get there by going to the project page. Press More Options and then select Project Preferences
In the Contact Forms to use on this project field: select the Contact Forms you want to use
Scroll down to the Choose a Contact Form to assign to the Enrolled state dropdown list and in that dropdown list, select the same Contact Form as one of the ones you chose above.
Press the Save button
You arrive back on the Project page
The Contact Form has now been successfully added to the project. You can now create a contact using this Contact Form.