I am a new 1976 Covette owner, how do I find out if the engine and transmission are original in my car.

Jim is right on with his idea.  I assume you know to check the VIN numbers and the block and side of transmission??

I have a 76 also (L48 with automatic) and finding the numbers on the transmission was a pain.  The 76 assembly manual points to where you need to look and it is different for each transmission (manual, 400 auto which came on the L82s, and 350 auto).  If you have the 350 auto like me, it is on the right hand side at the very edge of the transmission casting where it starts to angle up toward the block (and the numbers/letters are quite small - use a rag and bright light).  All the small blocks have the engine numbers on right forward side of the block where the block flange protrudes out slightly from the cylinder head.  If you don't see any numbers, it probably means the block was decked at some point.  When I finally figured out where to look, my tranny was replaced at some point and only the engine was orginal.