When it comes to publishing services with ArcGIS Server, the sharing process starts directly in ArcMap by clicking File > Share As > Service... which leads to the service editor. There you can specify important parameters (which can also be changed in the ArcGIS Server Manager), e.g. if the service will be dynamic or cached.
Later on, for administering ArcGIS Server it is recommended to use the ArcGIS Server Manager via the URL:
http://<myserver>:6080/arcgis/manager/

ArcGIS Server Manager
With the ArcGIS Server Manager you can
•add extensions like the Server Object Extension to the site
•activate the Server Object Extension in the capabilities of the SynOutputService
•manage services
ostop or restart a service
oedit permission for a service
osee the workspace of a service
odelete a service
•administer roles and users of your GIS server
•specify the level of detail for creating ArcGIS Server log messages
•retrieve ArcGIS Server logs in case of troubleshooting