What should you be thinking? Simple:
"I have 5 seconds of this guy's time."
... and then only if you're lucky. Once you realize that, everything else follows easily. Your first goal is to answer "what does this website do" in six words and stick that message in a place the user can't miss.
Next up is a clear call to action. A "Solve My Problem Now" button that takes up a third of the screen and can't be missed or mistaken.
Then you have 3 other elements to play with (At a maximum, a user will be able to process 5 things about a page, and you've already used up two). I'd go for a couple bullet points explaining benefits (not features), and some form of graphic showing that benefit happening in a spectacular way.
And that's it. That's all you get above the fold. Feel free to add more stuff, but make it low key and below the fold. The 4% of your visitors who are still around and curious can read it, but the rest will have bounced or clicked the signup button already. The facebook/twitter stuff you mention goes all the way down in the footer.
Examples (my own):
http://www.fairtutor.com/
http://www.twiddla.com/
Visit each one for 5 seconds, then come back here and see if you can remember what they do. If you can't, I've failed. If you can, I've probably still failed. But if you get stuck and click the "Go" button, I win.