To export the move-sidebar gadget, click on "Download" button, save the downloaded file, go to Special:Import on destination wiki and upload it. Then add the following to MediaWiki:Gadgets-definition page:

* move-sidebar[ResourceLoader|skins=wikitemp,tempstyle2,tempstyle3,tempstyle4|top]|move-sidebar.css

You must have appropriate permissions on destination wiki (including the right to edit system messages) and import from file uploads must be enabled.