If I understand your question correctly, you added a new form field to a class in the CMS.Membership module?
If that's the case, adding a form-field is not enough. You also need to override the relevant class in your own code and extend it in order to handle the submitted field's value.
From there you can capture the file in the new file upload field and save it to wherever you prefer. My preference would be a media-library but you may prefer you use local file storage.