To have a field marked as "required" simply set the flag "required" to true in installation file, in field definition.
array('name'=>'My field', 'type'=>'text', 'required'=>true),
More on this topic can be found
here.
Again - if you want to modify existing installation without reinstalling the module - check out *_field table and set "required" to 1 for each field you want to be obligatory.
Kind regards,
Arek