Buying Facebook stocks?

[A Nobody]

You DO NOT have to use a stock broker but you must use a brokerage firm (broker/dealer).

Assuming you're 18 years of age, you go to any brokerage firm's website and open an account.
Once you have the account open, (which will assign you an account number) you send in your check (with your account number noted on it) and then you can buy any stock you want

Yes, most security transaction involve a fee, especially if you are buying facebook.
And yes you must establish an account with the brokerage firm in order to enter into any transactions even if it is only a one time deal.

Keep In min that Facebook is an initial public offering (IPO) you will not buy the stock at that price, you will have to pay whatever the market is at the time you purchase it. The IPO is sold out so all buyers will be buying in the market just as you will have to do.