How is the amount of the transaction fee decided?
By everyone else's transactions fees. If everyone happens to be paying $100, you'll have to pay it too. Luckily everyone on the planet are greedy, and normally pay less than a penny.
I can be a bit more specific than that though. Bitcoin has a major disadvantage of only being able to process a maximum a 7 transactions a second (or otherwise notated as a maximum block size of 1MB). Transactions take up space in a block and transaction fees are how transactions "fight" their way into a block. Miners want money, so they pick people with the highest transaction fees. What this means is if too many people are making transactions and you have a very small fee or none at all (yes, you can choose to send bitcoins with a fee of 0) then you might not make it into a block and your transaction floats in purgatory forever (the network later rejects it entirely, you won't lose you money this way).
There is no way around this, unfortunately. It is a issue currently being discussed. Currently the only way to allow more transactions is to increase block size, in which the blockchain will start getting big, as in a few terabytes in less than a year, which is seen as detrimental to Bitcoin's status as "decentralized."
The sort of good news is that Bitcoin hasn't come close to approaching 7 transactions a second. In November 2013 it saw 3 per second.
What do I need to know before starting with Bitcoin? Because I went to the site and there was scary talk at the sign up and many privacy concern that I can't understand right now because I'm tired. What's the most important info for a noob?
That really depends on what you plan on doing with it. First off, there is no official Bitcoin site. Because Bitcoin is an open source, decentralized project, no one can claim rights to it or power over it. That said, you can trust this site, at least for now:
https://bitcoin.org/en/Read the introduction. Watch the video. Do all of it even if you've read this thread because Bitcoin is something you need to truly understand. It has never existed before and it can't be described using any existing technology. If you still have questions after that, let me know.
@Thork, Ben Franklin, Blanko have your discussion somewhere else, you are derailing the thread.