Overview & background
Each type of Project User has unique authorization to create, view, or edit forms and delete or reopen submitted forms. The permissions of each type of Project user that can take on the Forms feature are detailed below.
Who can create, view, edit, delete, re-open and push forms
Default Form permissions by 'Assignee' and project user type:
Note: If you are working on a form and there are people on the 'Distribution list' (see below) both Admins and Members can view the form. A Follower would have to be the form creator/assignee to view the form:
Who can view my form?
If the form can still be edited (is not in the 'Submitted' state or is still in the 'Open', 'Pending' or 'Draft' state), then Project Admins, the form creator, and the form assignee can view the form.
If the form is no longer editable (If the form is: 'Submitted', 'Closed', or 'Void'), Admins, Members, and the form assignee can view the form.
Who can delete forms?
Only Project Admins can delete forms. Deleted forms can be recovered from the Trash tab for 30 days following deletion. After 30 days the forms are permanently deleted and cannot be restored.
Why can't I edit my form?
It is likely the form was 'Submitted' or finalized by changing the state to one that is locked, which means the form is no longer editable. To edit it, the form status must be changed back to the 'Draft' state. Only Project Admins can "Un-submit" or Unlock forms so it may be necessary to contact a Project Admin to revert the form back to a 'Draft' state.
Account form templates
The Account owner and managers have access to the 'Templates' tab from the projects dashboard and are able to adjust the content of the account form templates. Project Admins can then pull the account form templates into projects, or push form templates to the Account. Take a look at this article for more information: Account Form Templates
Note: If you are not seeing the Form Templates in your Projects as is shown in the video above, you may need to check the status of the Account Form Template on the Account Home page. In order for the Forms Template to be pulled into the Project from the Account, the Status of the Template needs to be changed from "Unpublished" to "Published".
Manage Form Permissions & Statuses
Project Admins have the option to Manage Form Permissions and Statuses. Form Permissions dictate who can edit form attributes and form sections, and Form Statuses dictate whether or not the Form is editable. To adjust Form permissions:
Permissions:
Only the Creator, Admin, and assignee can edit the Form attributes - these include the Form Description, Status, Assignee, Date, and Due date. This setting cannot be adjusted:
Sections, or the fillable entries within the Lists and Tables in a form, can be adjusted - Admins can choose whether only the form Assignee or if All users can edit fillable entries within a form.
Note: If all users is selected under the can edit sections, all followers, even those not assigned to the form will be able to view and edit the forms created from the template.
Refer to the Custom Forms Article for more information about the Entries within the List and Table sections, as well as the Attachment and Signature sections.
Statuses:
Form Statuses by default are 'Draft' and 'Submitted' - these dictate when the form can be edited, and which Project User Permissions can make the form non-editable. Project Admins, however, have the option to edit the statuses associated with a Form -
Project Admins can customize at which stage of a form it is editable or not in the Form is editable column. All required fields must be filled before the form is moved into a 'non-editable' state:
Can enter status and Can exit status is a way to designate which permission levels are able to change the status of the form at that given moment:
By default, only Project Admins can move a form into a 'Submitted' state, but this can be adjusted as you see fit, depending on who you would like to edit the form, and at which stage: 
Project Admins can create New Statuses by selecting the '+New status' option in the bottom right corner: 
More information