this instructable covers using 7.10 (gutsy gibbon) it should work with most Ubuntu distros though.
Step 1: Getting the Required Stuff
ok first you need to go to http://www.adobe.com then click the "get flash" icon on the right hand side of the page. It should automatically detect the fact that you are using Linux and give you the correct file types.
click download, and save to disk the tar.gz file you DON'T want the .rpm or YUM files.
Step 2: Actually Installing It
try and play a video, it won't work thats what we are going to do now, make it work, over the next two steps!
go ahead and open the tar.gz file, and click extract, a new window will pop up, asking you where you want to extract it to, select your desktop (it should select your desktop by itself anyway).
Step 3: Installing It
anyway, go to the desktop, you will see a folder called the same thing as the tar.gz file you downloaded (something like install_flash_9_linux)
open that folder, you will see that there are two icons in that, click on the FlashPlayer-Installer Icon
now you should get a message, choose "run in terminal" now here is the first time that you are actually going to have to use a command line, and it is really easy!
make sure you read all the instructions as they come up, make sure you have no browsers running, that means Firefox Sea monkey etc.
when you see the "install action summary" press Y (yes) and enter, if you press Q it will give you a load of info about it (boring) or N will not install it (it means no).
let it do its thang, and when it is finished, close it and start firefox, go to youtube and viola
Step 4: After Thoughts
Also although this instructable can help you avoid using Ubuntu's command line (terminal) as much as possible it is a good idea to be able to use it and be relatively competent in its use, because there will be times when you have to use it!
but you will in time get to learn the basic commands such as "sudo apt-get install" etc in time, its all part of the Ubuntu experience (how corny does that sound)
I do read my comments so if this isn't working for you, please use the comments section and I shall endeavor to to help you, (after all it is part of the concept of Ubuntu, remember "I am because you are."