As someone that lives in EU (as in, not in USA) and has no clue about stock market: what would be the easiest way for me to get a couple of hundred € worth of stocks in FB? Is that even possible?
On top of that, "a couple of hundred €" is probably not enough money. The fees to buy stocks on the Nasdaq is usually in the tens of euro. You'll probably have between 10 and 50 euros of fees at the cheaper online trading platforms.
You can also call your traditional bank to buy the stocks but the fees would probably be higher.
Look into what is involved in buying stock in any American company from the EU. If you're still interested, you can pick up a few shares after it's trading on the exchanges.
It can be tricky to get into the IPO though. Don't know the details on those rules.