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).