Hi Webbe06,
Unlike Tyler I am not from Laminar Research; just a flight simmer from down under.
What did you purchase from Aerosoft?
If it was a digital version then follow the advice provided by tyler.
If it was a DVD set then there is no product key. You have to have Disc 1 inserted in your DVD drive at all times when running X-Plane. If you don't then it will automatically default you to a demo version with a "run-time" of 10 minutes. There is a key or code supplied in the DVD boxing but this a "ploy" or "con" to entice you to purchase other Aerosoft packages at a discount rate. I know because I was caught thinking the code was the product key.
Whatever format of X-Plane you have purchased you need to be connected to the internet. For the digital download, full time, and the DVD version on a regular basis as XP performs a silent background check to ensure you are running a legal version of the software.
Good luck.
Glenn