How do i install flash on my Mac version 10.6.6?

[Heidi]

Just got a new Mac a few days ago. I love it.The only thing I can't stand is that I'm having problems installing Flash player. Without it I can't watch Youtube videos, play certain games, etc. I go to the adobe website and do everything like I'm supposed to... I select Flash player under the download menu, I choose my operating system (mine is mac 10.6.6 So i choose version 10.4-10.6) and then i choose flash player 10.1 as it is the only version listed in the versions menu. I'm using Safari, (I also have firefox installed on my computer) and it says it's for Safari, Firefox, and Opera. Then I click "Download now". It says thank you , your download will start automatically...which it does. A little window popped up with a status bar in it. Then in the same window, the status bar is replaced with a little flash package logo and it says "Install Adobe Flash Player 7.6 MB" Also a little Flash player icon appears on the desktop that resembles a flash drive... I don't know what to do from here. If I double click the desktop icon another window pops up with a pic of the package and it says "install Adobe Flash player" if I double click that another window opens and asks if im sure i want to open the "install Adobe Flash player" application. (The same dialog box appears if i try to open it directly from the download window...the one the status bar was in) So I click "open", agree to the terms and click Install. It asks for my password, which I type in and click ok...then it shows a blue status bar that goes really fast and then says installation suceeded, so i click done...the dialog box disappears. I'm left with the flash player icon on the desktop (that looks a little like a flash drive) There is still a window open that has a pic of the flash player package and says "install Adobe Flash Player" and the window w/ the adobe website that i had to go to to get the player is still open. It didnt tell me to close any of the windows during installation, nor did it close any itself. Close all Safari browser windows I try going to youtube. It's still telling me i need to download flash player. So, I try going to Finder to see if it is installed...but that window is still up that says "install Adobe Flash Player" If I click on the Applications folder on the bottom of the screen, flash player isnt there and any time i try to click on the flash player icon on the desktop, it just makes that window come forward... what am I doing wrong? Even if i close that little window, and double click the flash player icon on the desktop it just opens that same window again...and if i click the thing inside the window it acts like its trying to download the flash player again, making another "are you sure you wasnt to open ..."window pop up again...it just keeps leading me in circles no matter what i do.. HELP