I quit social networking sites because they made my life significantly worse. If you really need to use them, you can, but don't worry. There is a wide variety of ways to use them, ranging from adding hundreds of people to just a few friends.
So should I just create an account and add every single person I am even tangentially acquainted with?
Yes, you can do this, but you don't have to. This is one reasonable way of using the site that a lot of people use, but it's also common to restrict things to people you know better.
Is there a feature on facebook where you can hide who your friends are?
YES. Absolutely. And it's an essential feature. If you do use Facebook please pay close attention to the privacy settings. You can make everything about yourself private, to the point where no one else, even your friends, can see anything except messages you specifically send them.
Is it appropriate to ask someone you just met to friend you?
Yes, it's pretty common to do this, though you may be surprised by how many people don't like to use these sites.
I am beginning to suspect that it is surprisingly common for intelligent, competent adults to somehow make it through the world for a few decades while missing some ordinary skill, like mailing a physical letter, folding a fitted sheet, depositing a check, or reading a bus schedule. Since these tasks are often presented atomically - or, worse, embedded implicitly into other instructions - and it is often possible to get around the need for them, this ignorance is not self-correcting. One can Google "how to deposit a check" and similar phrases, but the sorts of instructions that crop up are often misleading, rely on entangled and potentially similarly-deficient knowledge to be understandable, or are not so much instructions as they are tips and tricks and warnings for people who already know the basic procedure. Asking other people is more effective because they can respond to requests for clarification (and physically pointing at stuff is useful too), but embarrassing, since lacking these skills as an adult is stigmatized. (They are rarely even considered skills by people who have had them for a while.)
This seems like a bad situation. And - if I am correct and gaps like these are common - then it is something of a collective action problem to handle gap-filling without undue social drama. Supposedly, we're good at collective action problems, us rationalists, right? So I propose a thread for the purpose here, with the stipulation that all replies to gap announcements are to be constructive attempts at conveying the relevant procedural knowledge. No asking "how did you manage to be X years old without knowing that?" - if the gap-haver wishes to volunteer the information, that is fine, but asking is to be considered poor form.
(And yes, I have one. It's this: how in the world do people go about the supposedly atomic action of investing in the stock market? Here I am, sitting at my computer, and suppose I want a share of Apple - there isn't a button that says "Buy Our Stock" on their website. There goes my one idea. Where do I go and what do I do there?)