How do we control fields appearing while doing state movement like Assign or Approval?

We can do this by going to setting page of particular process ‘Workflow management’->‘States’. In this page you need to click under ‘Customize fields’ column for a particular state name for which you want to remove/add the fields. You can control the visibility by clicking the ‘Is Visible’ check box.

Please refer our online help link for more details - States