I am using an older version of dnn so this might not have the same wording as yours but here is what I would do.
1. go to the page while signed in as an administrator or super user.
2. click on settings under the page functions on the admin/super user banner
3. under basic settings, go to the permissions area
4. add the username of the person that you want to have permission and click add
5. Now select the view and edit check boxes.
6.scroll down and click update.
7. go to each module on the page and do the following:
7.1 click settings and then go.
7.2 under basic settings, permissions, uncheck inherit View permissions from page.
7.3 select who can view the module and edit the module for each module.
Let me know if this answers your question