I assume single use license. Go to Start, Programs, ArcGIS, ArcGIS administrator. Assuming you have already authorized Desktop, click authorize now, choose the second option which states something like "I have already authorized core licenses, now I would like to authorize extensions, follow the prompts. THEN, don't forget to start ArcMap, go to Customized > Extensions and select Spatial Analyst. If you don't you will get an error that it is not authorized, even though it IS authorized.
