Once you have selected a DOI to 'View' or 'Update' from the My DOIs tab, you will be navigated to a new tab for the selected DOI. 

If you have chosen to 'View' the DOI, the information displayed will be read-only. You can select the 'Enable Editing' link to enter into edit mode.
Read-only view of a DOI

If you have chosen to 'Update' the DOI, the URL and metadata displayed in the form will be editable. Once you have finished editing the DOI, select the 'Update' button at the bottom of the tab to apply your changes.

Editable view of a DOI

Note that when changing the URL, the new URL must conform to one of the domains registered with your account. To check your domains click the 'App ID Configuration' tab.