How do they determine how much Facebook is currently worth, and how does it currently make money? I'm confused as to how websites make money in general aside from advertisements.
What do you mean?
My understanding is that Facebook makes revenue by selling advertising, user data, and, I think, through in-app purchases.
To paraphrase Marc Faber: We're all doomed, but that doesn't mean that we can't make money in the process. Rabbi Lapin: "Let's make bricks!" Stephan Kinsella: "Say you and I both want to make a German chocolate cake."
Until recently, Facebook made practically all of their money from advertising (located at the far top column of the site). Recently, they started making some money from in-app sales, though I recon it's still a minor part.
I guess they might start charging app developers in future (who right now get free hosting plus a lot of free traffic) - but only if the owners decide this additional revenue is worth slowing down the rate of innovation in app development brought by "free riders".
In academic finance, it would be the present value of future cash flows.
Is all of the future income generated through assumed advertisements?
Oh yeah. For some reason I was thinking that Facebook had no advertisements yet, so I was curious as to how they paid employees, but that makes completely sense now.
Just to back up my previous claim: e.g., http://mashable.com/2011/01/17/facebooks-ad-revenue-hit-1-86b-for-2010/.
And I made a typo - the ads are in the right column, not top.