If you want to find out by looking at the MBA, you can determine whether it's a 1,1 Intel graphics or 2,1 Nvidia GPU by looking at the ports. If there are two ports of similar size, it's an original MBA (the mDVI looks similar to USB ports). If there is a USB port, a smaller port (Mini Display Port), and an audio plug, it's a rev B/C v 2,1 MBA.
To check further, go to the Apple and select "About this Mac" in the upper left hand corner. This will tell you the CPU and memory.
1.6 + 667 MHz DDR2 = Original MBA (probably HDD)
1.8 + 667 MHz DDR2 = Original MBA (probably SSD)
1.6 + 1067 MHz DDR3 = Rev B (probably HDD)
1.86 + 1067 MHz DDR3 = Rev B (probably SSD) or Rev C (HDD)
2.13 GHz + 1067 MHz DDR3 = Rev C (SSD)
Now, that tells you the easiest info to get to. If you need to dig further, select "More Info" on the About this Mac display box. This will tell if it's an original MBA or rev B/C MBA by stating 1,1 for original or 2,1 for rev B/C.
On the left side of the More Info box, select "Serial-ATA." This will finally tell you which drive you have for certain. Mine says "Apple SSD SM128." If it were an HDD it wouldn't specify SSD.
Remember to all, the quickest way to ensure it's not an original MBA is to look at the ports. One USB sized port with a smaller port and audio out jack is the rev B/C Nvidia MBA we all want. The original has what looks like two USB ports and an audio plug. The size of the mDVI port on the original is almost exactly the same size as a USB port.
Good luck.