Creating Group Fields with infoodle is essentially the same as creating People Fields, except the fields created are located under the Groups under the assigned Group Type and don't have as many options when creating them.
Manage fields for Groups is located under Administration > Custom fields:
See Manage Fields for more information on how to create fields for Groups.
Once the Group Field is created, then you will need to manage the Group Types that this field will be available under.
See Managing Group Fields for more information