WYMeditor versions leading up to and including version 1.1.1 introduced some major changes which made the library incompatible with Wysiwyg's implementation. The file structure was also changed, moving the main files out of a second 'wymeditor' subfolder up to the main library folder. Simply extract the WYMeditor archive to your sites/all/libraries folder as usual and Wysiwyg will recognize the correct structure depending on the detected installed version.
Note: Later versions of WYMeditor require a jQuery version newer than what Drupal 6 provides, even with the latest release of jquery_update.module installed. It is recommended not to upgrade unless you are using other means if loading jQuery.