All you have to do is go to the ArcGIS Server manager site at:
http://SERVER_NAME/ArcGIS/Manager/Default.aspx
In Services select the Manage Services:
Select the service you want to restart:
Click on restart:
Now just wait for it to finish:
When the process is done be sure to check the status of the service:
Started is good, Stopped is bad:
//TODO: Write a basic post on ArcGIS Server