Bitcoin QT Synchronizing

I wanted to try to document my experience with Bitcoin, not only for myself or others unfamiliar with Bitcoin, but for experienced Bitcoin users, who may not know what getting into Bitcoin is like for a new user. On this post I'm only covering my experience with installing and using the Bitcoin-Qt program, since there seems to be a good bit on what Bitcoin is, and repeating it here would seem redundant, especially because I'm not entirely sure enough about the more technical aspects to try to explain it sufficiently.
I use Linux Mint, so I went ahead and installed the bitcoin cli program, and found a ppa for Bitcoin-Qt and installed it. So far so good, program installs and is synchronizing...and synchronizing...and synchronizing. It ends up taking about two days (on and off, I turned my computer off for about 6-8 hours at one point). I'll admit that I don't understand how or why that takes so long, but I can see why that would be a turnoff for some people. But whatever, I finally get it up to date, and we're good to go! Now what? I start searching around online and find what appears to be the two best forums for Bitcoin, Bitcointalk.org and Reddit's /r/Bitcoin. They seem like pretty good starting points, so I start digging in and checking out this Bitcoin thing.

So, the Bonus Programs are a good way to get a little bit of bitcoins, but they're not any way to seriously make money. The important thing about them, to me, is that they helped me understand the concept of transferring and receiving Bitcoins. I had to give them a code, such as
"1A4f9eKk23CvPiCKkLKN44uiXyNu8Eyo55", which is one of the Bitcoin addresses I generated. I may be terribly inaccurate in this, but my understanding is that they send an amount of Bitcoins to that address, and once the payment has been confirmed by a certain number other Bitcoin programs (since there is no central program that verifies it), it is added to my balance. How long this takes depends on how many connections I have to other Bitcoin programs running that can verify that the transaction took place (but it is my understanding that all they know is that the transaction took place and that 0.0005 Bitcoins were given to me, not who I am specifically, I am only identified by that address I gave them). There's also apparently a very small fee involved with sending Bitcoins (something like 0.0005 BTC), but I don't know the details of this since I sent no Bitcoins, but that's something I'm sure I'll learn about another day.