If you were unlicensed when you passed the examp, you can go on the air as soon as your new callsign appears in FCC database.  

If you already were licensed and upgraded, you can use your new priveledges immediately, just be sure to add the appropriate call sign suffix if you are transmitting on a frequency that is only included with your new priveledges.   Those suffixes are "/AG" for those who upgraded to General Class, and  "/AE"  if you upgraded to Amateur Extra (often just called "Extra").  

When you ID on voice in the General Class parts of the band, it would sound like "KX0XXX temporary A G".  You can also use the word "stroke, or slash"  between your call and the upgrade indicator.  

Once your new license class is reflected in the FCC Database, then you can drop the upgrade indicators.