The first thing to do is make sure the group(s) have permission to upload to the given file upload directories. So- go to ‘Admin- Weblog Admin- File Upload Preferences’- edit the prefs for any folders you want to allow them to upload to. At the bottom of the page, you’ll spot group level permissions. Does the group(s) have permission there to upload to the folders they’re trying to upload to?
If they DO have permission there- what’s happening when they try to upload? What error messages are they getting and at what stage in the process?