The directions in http://docs.qgis.org/2.2/en/docs/user_manual/osm/openstreetmap.html#saving-osm-data seem to have been written before the OSM plugin was merged into QGIS proper. I can locate no OSM plugin or toolbar, and the vector menu only has options for opening a .osm file in QGIS.
Since the update of the OSM plugin, all editing and uploading functions of the plugin are removed.
The standard OSM editors have much better capabilities of editing and internal checking than QGIS can provide.
The manual page you mentioned has been forgotten to be dropped. Maybe underdark can do something about that.
Nowadays the best way to transform GIS data to OSM is to open it (GML, SHP, ...) in JOSM with OpenData Plugin (1) activated and, if you want, you can save it to *.osm format.