If you want to edit a plan, open it by clicking on the card. Click on the pen icon to edit and the card opens in edit mode and you can do the changes you want.
Earlier I said that you add an Assignment to a plan and to do so you open the plan for editing. How you add the Assignment is described here.
When you are done with your editing you click on Save, or Cancel if the editing was not needed. When you are in editing mode, it is not possible to do anything else in Newsroom Planner before you close the editing.