For the wiki, to enable attachments you must:
1)Wiki attachments must have been enabled at Administration:Wiki Attachments
(As of 1.9.7 this checkbox does not appear in the list with the rest of the features)
2)Permissions wiki_view_attachments, and wiki_attach_files must be present in at least one of the Groups the user is assigned to.
These two permissions allow uploading and viewing of attachments. Deleting an attached file is only possible for the one who uploaded the file. If you want, that everyone is able to delete file attachment you need to set tiki_p_wiki_admin_attachments additionaly or to a group that shall be allowed to delete.