Before jumping into configuration options, it is useful to remember that every field in your content type comes with a default widget. Thus you only need to go through the setup process when the current widget inhibits the flow of the editorial team.
To set a widget (or change its options), open your Content type, then for each field, navigate to Settings > Appearance and select an appropriate widget. The changes will take effect once the new field settings are saved and the content type is (re)published.
At the moment of writing, it is not possible to configure widgets via API.
NOTE: Some widgets are only open to customers on Enterprise plans and have to be activated prior to use by contacting our support staff.